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sar  Female  College. 

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late myself  on  my  selection  of  it  as  a  text-book."— R.  P.  DUNN,  Brown  Uni- 
versity. 


FROM 

STEPHEN    SEARS, 

NEW  ENGLAND  AGENT  FOR 

SHELDON  &  co.'s  PUBLICATIONS, 

No.  41    Franklin   Street, 

BOSTON. 


Th 
T 


A 


PRIMARY 


AEITHMETIC, 


AND 


TEACHER'S  MANUAL, 


WITH 


CLASS  AND  SEAT  EXERCISES  GRADED  WITH  REFERENCE 

TO   THE  VARIOUS   STAGES  OF  THE   PUPIL'S 

ADVANCEMENT  IN   READING. 


BY  EDWARD   OLNEY, 


PROFESSOB  OF  MATHEMATICS  IN  THE   UNIVERSITY  OF    MICHIGAN,   AND  AUTHOR 
OF  A  SERIES  OF  MATHEMATICAL  TEXT-BOOKS. 


- 

? 

• 


NEW    YORK: 


& 
1875. 


OLNEY'S  SERIES  OF  MATHEMATICS. 


OLNEY'S    PRIMARY   ARITHMETIC. 
OLNEY'S    ELEMENTS    OF    ARITHMETIC. 
OLNEY'S  SCIENCE  OF  ARITHMETIC.     (In preparation) 

TEACHER'S   HAND-BOOK   OF    ADDITIONAL    EXAMPLES    AND 
EXERCISES.     (In  press.) 

INTRODUCTION     TO    ALGEBRA $r  oo 

COMPLETE    SCHOOL    ALGEBRA i  So 

TEST    EXAMPLES    IN    ALGEBRA 75 

OLNEY'S    HIGHER    MATHEMATICS. 

UNIVERSITY    ALGEBRA 200 

ELEMENTS    OF    GEOMETRY .        .  i  50 

ELEMENTS    OF    TRIGONOMETRY i  50 

GEOMETRY  AND  TRIGONOMETRY,  UNIVERSITY  EDITION.  300 

GENERAL     GEOMETRY    AND     CALCULUS  .  ...  2  50 


Entered,  according  to  Act  of  Congress,  in  the  year  1874,  by 

SHELDON    &    CO., 
in  the  Office  of  the  Librarian  of  Congress,  at  Washington. 

Copyright,  1875,  SHELDON  &  Co. 


Electrotyped  by  SMITH  &  McDoucAL,  82  Beekman  St.,  N.  Y. 


U1I7BII       7 


PREFACE. 


IT  is  thought  that  the  spirit  of  this  book,  and  the  manner  of 
using  it,  will  be  so  evident,  as  the  teacher  reads  it  over,  that 
few  prefatory  words  are  needed.  The  following  are  some  of  the 
leading  principles  by  which  the  author  has  been  guided.  How 
they  have  been  wrought  out  can  be  seen  only  by  examining  the 
book  itself. 

1.  A  text-book  for  schools  should  be  arranged  with  reference 
to  sound  principles  of  teaching,  and  to  convenience  of  use  in  the 
school-room,  quite  as  much  as  to  the  principles  of  the  science 
which  it  develops. 

2.  One  thing  at  a  time  is  the  fundamental  maxim  of  primary 
teaching.     Each  exercise  must  have   a   single,  clearly  defined 
purpose. 

3.  Unity  of  purpose  and  almost  infinite  diversity  of  means  char- 
acterize the  most  successful  teaching  of  the  young. 

4.  The  young  child  must  be  furnished  something  to  do.     His 
hands,  his  eyes,  and,  as  much  as  may  be,  his  tongue  and  his 
whole  body,  must  be  busied  with  the  work  in  hand. 

5.  In  a  well-conducted  primary  school,  as  careful  attention 
will  be  given  to  secure  profitable  employment  for  the  pupils  in 
the  seats,  as  to  the  conduct  of  the  class  exercises. 

6.  The  cases  are  exceptional,  and  very  rare,  in  which  much 
labor  or  time  need  be  bestowed  in  order  to  awaken  in  the  mind 
of  the  child  the  conception  of  number.     The  recognition  of 
number  is  one  of  the  most  simple,  earliest  developed — in  fact, 


iv  PREFACE. 

most  nearly  innate — of  all  our  mental  acts.  The  child  who  has 
learned  to  count  10  by  means  of  objects,  has  as  well-defined, 
practical  notions  of  number,  as  he  needs,  and  as  he  advances 
with  the  simple  processes  of  combination,  his  conceptions  will 
enlarge  as  occasion  requires. 

7.  There  are  two  distinct  mental  processes  required  in  obtain- 
ing a  mastery  of  the  elementary  combinations  of  numbers : 

1.  The  method  In/  which  we  determine  what  the  result  of  the  com- 
Mnation  is,  and 

2.  The  fixing  of  that  result  in  the  memory. 

Thus,  it  is  one  thing  for  the  pupil  to  learn  how  he  may  find 
out  how  many  6  times  7  makes,  and  quite  another  thing  to  fix 
this  product  in  his  mind.  The  former  is  a  process,  which  the 
child  who  can  count  will  readily  learn,  and  which  he  will  always 
apply  with  pleasure.  The  latter  is  a  pure  act  of  memory,  and 
the  pupil  needs  all  the  help  an  ingenious  teacher  can  devise,  to 
save  it  from  becoming  intolerable  drudgery.  In  a  single  lesson, 
the  child  who  can  count  one  hundred,  will  learn  to  make  the 
Multiplication  Table  as  far  as  10  times  10.  But  to  remember 
these  100  products,  so  that  they  can  be  instantly  named,  is  no 
less  a  task  than  to  memorize  the  answers  to  any  other  100  prob- 
lems. The  same  may  be  said  of  the  Addition,  Subtraction,  and 
Division  Tables ;  for  they  are  none  of  them  well  learned  until 
the  results  can  be  recalled  without  any  mental  process  except 
the  instantaneous  act  of  the  memory. 

8.  To  perceive  and  to  remember  are  the  chief  mental  exercises 
of  the  grade  of  pupils  for  which  this  book  is  prepared.     Such 
pupils  cannot  be  expected  to  give  formal  statements  either  of 
definitions,  processes,  or  reasons;  and  much  less  can  they  obtain 
conceptions  and  learn  processes  from  abstract  statements.    Hence, 
formal  definitions,  rules,  and  processes  of  reasoning  are  out  of 
place  in  such  a  book. 

9.  Usually  the  child  who  cannot  count  cannot  read ;  and  the 
processes  of  learning  to  read  and  learning  the  elementary  com- 


PREFACE.  v 

binations  of  numbers  are  going  on  at  the  same  time.  Accord- 
ingly, in  this  book  the  first  27  pages  are  addressed  to  the 
Teacher;  the  next  90  are  addressed  to  "pupils  reading  simple 
•words ;"  and  the  remainder  of  the  book  assumes  that  the  pupil 
has  learned  to  read  tolerably  well. 

10.  According  to  the  decimal  notation,  the  fundamental  com- 
binations embrace  only  numbers  below  and  including  10.     To 
such  combinations  this  book  is,  therefore,  confined. 

11.  One  is  more  interested  in  what  he  has  made  himself,  than 
in  that  which  is  furnished  by  another.     Hence  the   pupil   is 
taught  how  to  make  the  Addition,  Subtraction,  Multiplication, 
and  Division  Tables  for  himself,  and,  having   made  them,  to 
study  his  own  work.    None  of  these  tables  are  given,  except  in 
form,  in  this  book. 

12.  From  objects  in  sight  and  in  hand  to  objects  out  of  sight 
— from  the  concrete  to  the  abstract,  from  the  known  to  the  un- 
known, by  short  and  easy  steps — an   arrangement  which  will 
make  each  advance  include  a  practical  review,  etc.,  are  princi- 
ples so  well  established  that  no  intelligent  teacher  will  counte- 
nance the  violation  of  them. 

The  teacher  who  is  familiar  with  the  methods  of  the  Kinder- 
garten will  recognize  the  spirit  of  those  methods  on  every  page 
of  this  book.  Indeed,  it  has  been  a  leading  purpose  to  embody 
this  spirit  in  forms  which  are  practicable  for  use  in  our  ordinary 
Primary  Schools. 

EDWAUD  OLNEY. 

UNIVERSITY  OF  MICHIGAN,  December,  187k. 

NOTE. — Since  the  plates  of  this  book  were  first  cast,  the  whole  book,  in  com- 
plete form,  has  been  thoroughly  examined  by  a  number  of  practical  tcnchers  in 
different  parts  of  the  country,  and  carefully  revised.  The  exceedingly  liberal 
spirit  of  the  publishers  has  allowed  the  author  to  make  such  revision  to  any 
extent  he  desired.  To  Prof.  N.  A.  CALKINS,  of  the  New  York  City  Normal 
School,  the  author  is  very  greatly  indebted  for  valuable  suggestions  in  connec- 
tion with  this  work  of  revision.  E.  O. 


INTRODUCTION. 


ORGANIZATION    AND     EXERCISES     OF    A 
PRIMARY     SCHOOL. 

much  attention  has  been  given  of  late  to  primary  teaching, 
and  principles  and  methods  have  been  so  rapidly  developed, 
that  the  author  has  thought  that  a  synopsis  of  a  few  of  these 
results  would  be  acceptable  to  the  teacher.  The  preface  recites 
some  of  the  established  principles ;  it  is  the  purpose  of  this  in- 
troduction, and,  in  fact,  of  this  book,  to  exhibit  in  outline  an 
embodiment  of  such  principles  in  method. 

So  great  is  the  diversity  among  our  Primary  Schools,  that  it 
is  practically  impossible  to  present  a  schedule  which  is  adapted 
to  all.  What  is  designed  in  this  attempt  is  to  indicate  some- 
what of  the  plan  of  organization  and  course  of  exercises  found 
in  our  best  Primary  Schools  in  towns  of  3,000  to  8,000  inhabit- 
ants, where  the  schools  are  graded  into  4  or  5  departments.  In 
the  larger  cities,  where  there  are  two  or  more  primary  grades, 
the  oral  exercises  can  be  more  frequent  for  each  class,  and  still 
greater  variety  will  be  practicable.  Nevertheless,  the  spirit  and 
general  features  of  the  scheme  may  be  much  the  same  in  all. 

Such  a  school  as  is  here  described  will  consist  of  50  or  60 
pupils  arranged  in  3  classes,  styled  respectively  the  "  A  "  class, 
"B"  class,  and  "C"  class,  the  first  being  the  most  advanced, 
and  the  last  the  least.  The  pupils  of  each  class  will  be  seated 
together,  as  seen  in  the  cut  on  page  5,  where  the  "  A "  class 
occupies  the  two  forms  at  the  left,  the  "  B  "  class,  which  is  at 


INTRODUCTION.  vii 

the  counting  table,  occupies  the  two  centre  forms,  and  the 
"  C  "  class  the  two  right-hand  forms. 

The  age  of  the  "  C  "  class  will  vary  from  5  to  7,  and  pupils 
will  be,  on  an  average,  about  a  year  in  each  class.  The  "  A  " 
class  will  usually  be  found  reading  in  what  is  called  the  u  Third 
Reader,"  and  will  be  able  to  learn  easy  lessons  in  descriptive 
subjects,  as  Natural  History  and  Geography. 

No  exercise  should  occupy  more  than  15  minutes,  and  with 
the  younger  classes  many  of  the  class  exercises  need  not  exceed 
5  or  8  minutes.  Ten  minutes  are  assigned  to  most  of  the  sepa- 
rate exercises  in  the  schedule.  Time  saved  by  the  shorter  ex- 
ercises will  give  opportunity  for  inspection  of  work,  singing,  or 
any  of  the  numerous,  nameless  things  which  need  attention. 

This  plan  supposes  that  the  pupil  will  be  kept  constantly 
busy,  recreation  being  as  regularly  provided  for  as  work.  "  st." 
means  "exercise  in  seat,  "cl."  means  "class  exercise,"  and 
"  B — B  "  means  work  on  the  pupils'  blackboard.  The  class 
exercises  are  printed  in  full-faced  type. 

Part  of  the  writing  exercises  will  be  for  the  purpose  of  learn- 
ing to  write,  and  part  for  the  purpose  of  learning  to  spell. 
The  former  will  usually  be  from  copy,  and  the  latter  from  dic- 
tation by  the  teacher  as  she  is  about  her  other  work. 

The  drawing  exercises  will  comprise  geometrical  forms, 
tracing  from  copies,  simple  natural  objects,  and  outline  map 
drawing. 

The  oral  exercises  will  be  largely  what  is  known  as  "  Object 
Lessons."  These  will  be  on  various  subjects,  such  as  color, 
form,  common  properties  of  bodies,  direction,  etc. 

The  "  A,"  "  B,"  and  "  C  "  classes  as  here  designated  corres- 
pond with  the  1st,  2d,  and  3d  Grades,  or  years,  respectively,  of 
the  system  now  coming  into  use  in  many  of  our  Graded  Schools. 
In  the  larger  of  these  schools  it  is  assumed  that  each  grade  will 
be  divided  into  two  Divisions, 


PROGRAMME  FOR  A  DAY  IN  A  PRIMARY  SCHOOL, 


TIME. 

"A"  CLASS. 

"B"  CLASS. 

"C"  CLASS. 

9      to   9:15 

Opening    Exercises. 

9:15  to    9:25 

Writing,  st. 

Reading,  st. 

Reading,  cl. 

9:25  to   9:35 

Reading,  st. 

Reading,  cl. 

Arithmetic,  st. 

9:35  to   9:45 

Reading,  cl. 

Drawing,  st. 

Printing,  B—  B. 

9:45  to   9:50 

Gymnastics,  and  Oral  Concert  Exercises. 

9:50  to  10 

Drawing,  B—  B. 

Arithmetic,  st. 

Arithmetic,  cl. 

10      to  10:10 

Arithmetic,  st. 

Arithmetic,  cl. 

Drawing,  st. 

10:10  to  10:20 

Arithmetic,  st. 

Writing,  st. 

Oral    Teaching. 

10:20  to  10:40 

Recess. 

10:40  to  10:50 

Arithmetic,  cl. 

Drawing,  B—  B. 

Writing,  st. 

10:50  to  11 

Geography,  st. 

Reading,  st. 

Reading,  cl. 

11      to  11:10 

Geography,  st. 

Reading,  cl. 

Drawing,  st. 

11:10  to  11:20 

Geography,  cl. 

Drawing,  st. 

Arithmetic,  st. 

11:20  to  11:30 

Gymnastics,  and  Oral  Concert  Exercises. 

11:30  to  11:40 

Writing,  st. 

Arithmetic,  st. 

Oral  Teaching. 

11:40  to  11:50 

Arithmetic,  st. 

Arithmetic,  cl. 

Printing,  st. 

11:50  to  12 

Arithmetic,  cl. 

Printing,  st. 

Drawing,  B—  B. 

2      to   2:10 

Writing,  st. 

Reading,  st. 

Reading,  cl. 

2:10  to   2:20 

Nt.  History,  st. 

Reading,  cl. 

Arithmetic,  st. 

2:20  to   2:30 

Nt.  History,  cl. 

Writing,  st 

Printing,  B—  B. 

2:30  to   2:45 

Gymnastics,  Stories,  and  Moral  Lessons. 

2:45  to    2:55 

Arithmetic,  st. 

Arithmetic,  st. 

Arithmetic,  cl. 

2:55  to   3:05 

Arithmetic,  st. 

Arithmetic,  cl. 

Writing,  st. 

3:05  to   3:20 

Recess. 

3:20  to   3:30 

Arithmetic,  cl. 

Drawing,  st. 

Drawing,  st. 

3:30  to    3:40 

Drawing,  st. 

Spelling,  st. 

Oral    Teaching. 

3:40  to    3:50 

Spelling,  st. 

Spelling,  cl. 

Printing,  st. 

3:50  to   4 

Spelling,  cl. 

Writing,  st. 

Drawing,  st. 

SECTION    I. 

COUNTING,  AND  READING   AND  WRITING   NUMBERS  FROM 

ONE  TO  ONE  HUNDRED, 


THIS  Section  is  addressed  to  the  Teacher.  It  is  presumed  that 
pupils  who  cannot  count,  cannot  read;  and  hence  that  the  text  of 
a  book  can  be  of  no  service  to  them.  The  pictures  in  this  section 
will  be  useful  to  the  pupils,  as  will  appear  in  the  progress  of  the 
lessons.  Hence  the  pupils  will  need  the  book  from  the  beginning. 


2  EXERCISES  IN  NUMBERS   FOR 

The  lessons  of  this  section,  however,  will  be  wholly  oral.  We 
call  this  class  of  pupils  the  "C"  class,  the  lowest  grade  in  the 
Primary  School.  (See  Introduction.) 

Appliances. — 1-  A  good  Blackboard,  crayons,  rubber, 
and  pointer,  for  the  teacher's  use.  The  blackboard  should  be 
about  3  feet  by  9. 

2.  A  Table  about  3  feet  by  6,  so  arranged  that  the  top  can  be 
inclined  towards  the  class,  and  low  enough  so  that  children  of  5  or 
6  years  can  see  its  surface,  as  they  stand  around  it,  and  can  get 
their  hands  on  it  conveniently. 

3.  One  Hundred.  Counters.      Tasty  counters  can  be  cut 
from  bright  colored,  heavy  card-board.      They  should  be  about 
%  of  an  inch  square  ;  or,  if  circles,  about  the  same  in  diameter. 
Common  wooden  button  molds  will  answer.     Whatever  is  used 
should  be  neat  and  convenient,  but   so  simple  as  not  to  attract 
undue  attention.     Small  bundles  of  splints  are  much  used. 

4.  A  Numeral  Frame— a  necessity  in  a  Primary  School. 

5.  A  Long   Blackboard  on  the  sidewall,  so  low  that  chil- 
dren of  this  age  can  write  on  it  easily,  and  long  enough  for  18  or 
20  pupils  to  stand  before  it  at  once,  and  write  on  it. 

6.  Each  pupil  needs  a  Slate  and  Pencil. 


LESSON    I. 

Purpose. —  To  teach  to  Count  from  One  to  Fen. 

Method. — Class  Exercises.  While  the  teacher  stands  behind 
the  Counting  Table,  and  the  class  is  gathered  around  it,  as  repre- 
sented in  the  picture,  let  the  teacher  have  ten  counters  lying 
together  on  the  table,  and  moving  out  one  of  them,  ask,  "  How 
many  is  that  ? "  When  this  is  answered  by  all,  move  out  another, 
and  placing  it  with  the  first,  ask,  "  How  many  have  we  now  ?  "  In 
this  way  see  how  far  any  of  them  can  count.  If  all  can  count  ten, 


PUPILS    WHO    CANNOT  READ.  3 

readily,  there  is  no  need  of  spending  more  time  on  the  exercises 
in  this  lesson.  But  class  answers  must  not  be  depended  upon  for 
determining  this — each  pupil  must  be  questioned  separately,  while 
all  look  on,  and,  when  occasion  serves,  help. 

If  few,  or  none  of  them,  can  count  ten,  the  work  of  teaching 
must  be  continued  till  all  can  count  thus  far,  readily.  Use  the 
counters  as  above,  having  the  pupils  count  in  concert,  at  first,  as 
the  teacher  moves  out  the  counters.  Then  encourage  individuals 
to  try  it.  "  Now,  who  can  count  four  ?  "  "  Well,  Jane,  count  out 
four  of  the  counters."  "  Who  else  can  do  it  ?  "  "  Who  else  ?  " 


"Who  can  count  out  seven  counters?"  "Well,  James,  you  may 
try  it."  "Who  else?"  etc.,  etc.  Vary  the  exercise  by  having 
the  pupils  count  marks,  or  dots,  as  you  make  them  on  the  board. 
Also,  if  they  know  any  letter,  as  o,  make  several  o's  and  let  them 
count  them.  (Use  letters  for  this  purpose  as  fast  as  they  are 
learned.}  Have  them  count  the  pupils  in  the  class,  the  buttons  on 
their  jackets,  the  objects  in  this  picture,  etc. 
As  another  exercise,  use  the  pictures  on  pages  5  and  8.  "  All 


EXERCISES 


NUMBERS  FOR 


find  the  boys  in  the  picture."  "  How  many  have  found  them  ?  " 
(Hands  raised  to  indicate.)  "  Count  the  boys  (silently)."  "Who 
can  tell  how  many  boys  there  are?"  (Hands  raised.)  "Sarah, 
tell."  "Mary,  count  them  aloud."  So  proceed  with  other  objects 
found  in  the  pictures. 

It  will  be  serviceable  as  a  class  exercise  to  have  the  class  re- 
peat the  numbers  in  concert,  while  you  beat  with  the  hand,  bring- 
ing the  right  hand  down  into  the  open  palm  of  the  left  at  each 
count.  Thus  teacher  and  class  count  together.  Class  count 
alone,  while  the  teacher  beats.  Class  beat  and  count,  while 
teacher  only  beats.  Such  exercises  as  these  will  be  serviceable 
mainly  in  teaching  the  names  and  succession  of  the  numbers ;  but 
this  is  no  small  part  of  the  problem. 

The  Numeral  Frame  is  very  convenient  in  teaching  counting. 

Teacher  hold  it  up  and  slide 
out  the  balls  one  by  one, 
as  the  class  counts.  Pupils 
take  the  pointer  and  slide 
out  the  balls  and  count,  or 
use  their  fingers  if  they  can- 
not handle  the  pointer.  For 
other  uses  of  this  important 
instrument  see  pages  9,  13, 
16, 18,  19,  20,  27,  31,  etc. 

Another  exercise  will  con- 
sist of  questions  like  the  fol- 
lowing :  "  How  many  eyes 
has  each  of  you  ?  "  "  How 
many  feet?"  "How  many 

noses  ?  "  "  How  many  fingers  on  one  hand,  without  the  thumb  ?  " 
"How  many  with  the  thumb?"  "How  many  on  both  hands, 
without  the  thumbs?"  "How  many  with  the  thumbs?"  etc. 
This  exercise  is  more  purely  mental  than  the  preceding,  inas- 
much as,  in  this,  the  pupils  are  expected  to  count  the  objects 
without  touching  them,  or  even  looking  at  them.  It  should  be 
extended  to  objects  outside  of  the  school-room  (out  of  sight). 
Thus,  "How  many  eyes  has  a  cow?"  "How  many  legs?" 


PUPILS    WHO    CANNOT   READ. 


~.  ".":•>      -v,,       ra.«5S£iiC',r,/Is»  \ 


6  EXERCISES   IN  NUMBERS   FOR 

"How    many  brothers    have    you?"      "How    many    sisters?" 
"  How  many  brothers  and  sisters  in  all  ?  "  etc. 

Seat  Exercises. — While  in  the  performance  of  other  duties, 
you  may  say  to  the  "  C  "  class,  "  The  '  C  '  class  may  take  out  their 
slates,  very  carefully"  After  a  little  while,  when  they  are  all 
ready,  say,  "  Each  one  make  three  marks  on  his  slate."  (To  be 
made  thus,  /  /  /.  Perhaps  it  may  be  necessary  to  show  them  how, 
by  placing  groups  of  marks  in  various  positions  on  the  black- 
board, and  instructing  the  pupils  to  make  them  in  similar  positions 
on  their  slates.)  Again,  after  a  little  time,  say,  "  Each  member  of 
the  '  C'  class  make  four  marks,"  etc.,  etc. 

The  exercise  may  be  varied  by  having  dots  made,  instead  of 
marks.  Better  still,  if  they  know  how  to  make  any  letter,  as  e,  by 
having  them  make  five  e's,  seven  e's,  etc. 

Vary  it  again  by  having  the  pupils  open  to  the  pictures  on  pages 
5  and  8,  and  tell  them  to  make  as  many  marks  as  they  can  find 
dogs.  As  many  as  they  can  find  kittens,  etc. 

Cautions  and  Suggestions.  — Though  this  (learning  to 
count  ten)  is  called  one  lesson,  it  will  require  several  days,  with 
several  class  exercises  each  day,  for  pupils  who  know  nothing  of 
counting  at  the  outset,  to  master  it.  No  class  exercise  should 
occupy  more  than  5  or  10  minutes  with  this  grade  of  pupils.  The 
seat  exercises  are  quite  as  important  as  the  class  exercises.  BE 

SURE  AND  ALWAYS  INSPECT  THE  WORK  WHICH  THEY  ARE  RE- 
QUIRED TO  DO  ON  THEIR  SLATES.  See  that  they  do  their  best, 
and  do  not  merely  scribble.  Do  not  try  to  teach  anything  but 
counting  at  this  time.  Defer  teaching  the  characters  (figures), 
and  how  to  make  them,  till  another  time.  Do  not  distract  their 
attention  with  ideas  of  adding,  counting  backwards,  or  subtracting. 
ONE  THING  AT  A  TIME.  Nor  need  any  special  effort  be  made  to 
give  the  pupils  the  idea  of  number.  If  this  idea  is  not  innate, 
they  will  get  it  from  the  above  and  kindred  exercises.  Generally, 
one  form  (or  at  most  two)  of  class  exercise  at  a  time  is  enough. 
So  also  of  a  seat  exercise.  Short,  single,  clear,  pointed,  lively— 
these  are  the  characteristics  of  a  good  exercise. 


PUPILS    WHO    CANNOT   READ. 


LESSON     II. 

.—  ^?  teacfi  the  Names  and  Meaning  of 
the  Figures, 


Also  to  review  the  preceding  lesson  in  connection  with  this. 

Method.  —  Class  Exercise.  With  the  class  around  the  Count- 
ing Table  and  before  the  teacher's  Blackboard,  as  represented  in 
picture,  page  1,  make  figure  /  on  the  board  (make  a  simple,  in- 
clined, straight  line,  not  /,  nor  any  elaborate  form).  Then  say, 
"  Children,  this  means  one"  Pointing  to  it,  ask,  "  What  does  this 
mean  1"  •"  James,  put  out  as  many  counters  on  the  table  as  this 
means."  "  Jane,  show  me  as  many  fingers  as  this  means  "  (always 
pointing  to  the  figure  when  the  question  is  asked). 

Again,  make  the  figure  2  (in  this  simple  form),  and  repeat  the 
questioning  as  above.  Thus,  first  telling  them  that  it  means  two, 
ask  them,  "  What  does  this  mean?"  "  Hold  up  as  many  fingers 
as  this  means."  "  Mary,  pick  up  as  many  counters  as  this  means." 
So  "  question  back  "  what  you  have  told  them.  Do  not  be  in  a 
hurry.  Put  a  great  variety  of  questions,  to  the  class,  and  to  each 
member  of  the  class.  But  let  each  question  be  directed  to  the  one 
end  of  fixing  in  the  mind  the  fact  that  the  figure  2  means  two. 
Do  not  call  the  figure  by  name,  but  point  to  it  and  say,  "  As  many 
as  this  means." 

Now  put  both  1  and  2  on  the  board.  Pointing  to  1,  say,  "  How 
many  does  this  mean  ?  "  "  Each  show  me  as  many  hands  as  this 
means."  "  Each  pick  up  as  many  counters  as  this  means."  In 
like  manner  point  to  2,  and  question  and  exercise  the  class. 

Proceed  in  like  manner  with  3.  This  will  be  enough  for  one 
exercise.  (It  may  be  too  much  for  some  classes.) 

Seat  Exercise.  —  When  the  time  comes  for  this  exercise,  with- 
out turning  aside  from  other  duties,  say,  "  The  '  C  '  class  may  take 


8 


EXERCISES   IN   NUMBERS  FOR 


PUPILS    WHO    CANNOT   READ.  9 

out  their  slates."  Put  the  figure  2  on  the  board.  Say,  "  Each 
make  as  many  marks  (dots,  e's,  m's,  a's,  see  preceding  lesson)  as  this 
means."  In  two  or  three  minutes,  put  the  figure  1  on  the  board 
and  proceed  in  the  same  manner.  In  like  manner,  after  a  short 
interval,  put  3  on  the  board  and  direct  as  before. 

Be  sure  and  inspect  the  work  after  it  is  done. 

A  Second  Class  Exercise  will  teach  the  meaning  of  the  figures 
4,  5,  and  6. 

A  Second  Seat  Exercise  like  the  above  will  give  them  practice 
on  it. 

A  Third  Class  Exercise  and 

A  Third  Seat  Exercise,  both  similar  to  the  above,  will  complete 
this  part  of  the  lesson. 

A  Fourth  Class  Exercise  will  teach  them  that  The  names  of  the 
figures  are  the  same  as  their  meaning. 

A  Fourth  Seat  Exercise  may  be  given  by  telling  them  to  make  as 
many  marks  (dots,  e's,  m's,  o's,  see  Lesson  I)  as  figure  5  means. 
As  figure  6,  etc. 

Cautions  and  Suggestions.— Do  not  let  the  exercises  be- 
come monotonous.  Strive  to  have  the  pupils  come  to  them  as  to 
something  which  they  enjoy.  Requisitions  which  can  be  met  by 
doing  something,  will  be  relished.  Thus,  "  All  clap  hands  3  times." 
"  All  stamp  as  many  times  as  this  "  (pointing  to  a  figure).  Count- 
ing in  connection  with  gymnastic  exercises,  and  the  like,  will 
enable  you  to  accomplish  several  things  at  once,  and  aid  in  keep- 
ing up  an  interest. 

The  exercises  of  this  lesson  have  been  written  out  thus  in  detail 
to  show  how  minute  the  subdivisions  really  need  to  be  made. 
(See  first  Caution  under  the  last  lesson.)  Generally,  this  subdi- 
vision will  be  left  to  the  discretion  of  the  teacher.  Some  classes 
will  need  shorter  exercises  than  others — that  is,  will  be  able  to 
take  in  fewer  new  ideas. 

The  Numeral  Frame  is  very  useful  in  teaching  the  meaning 
of  figures.  First  let  the  teacher  move  the  balls  to  show  how 
many  any  given  figure  represents  ;  subsequently,  let  the  pupils  do 
the  same. 


10         EXERCISES   IN  NUMBERS   FOR 

LESSON    III. 

Purpose. — 2"o  teach  to  make  the  Figures, 

'/ 

Also,  to  review,  in  connection  with  this,  the  two  preceding  lessons. 

Method. — Take  the  figures  of  simplest  form  first.  They  will 
then  be  taken  about  in  this  order — 1,  7,  4,  6,  9,  2,  3,  5,  8. 

Let  the  first  Class  Exercise  be  to  teach  how  to  make  1,  7,  and  4. 
"  Who  can  tell  me  how  to  make  the  figure  which  means  one  ?  " 
Place  the  crayon  point  on  the  board,  and  lead  the  pupils  to  say 
"  Mark  right  down."  Make  it  too  long — a  foot  long — and  have 
them  tell  you, "  It  is  too  long."  Make  it  crooked,  and  let  them 
correct  you.  Incline  it  the  wrong  way,  and  let  them  tell  what  is 
the  matter  with  it.  Then  ask  each  of  them  in  turn  to  step  to  the 
board  and  make  figure  one.  Call  it  sometimes  "  figure  one,"  and 
sometimes  "  the  figure  which  means  one."  Ask  frequently, "  What 
is  the  name  of  this  figure  ?  "  "  What  does  it  mean  ?  "  "  Show  me 
as  many  counters  as  it  means  ?  "  "  Clap  hands  as  many  times  as 
it  means,"  etc. 

When  a  figure  has  been  made  on  the  board  by  a  pupil,  let  the 
class  notice  wherein  it  is  not  right,  and  let  those  who  notice  de- 
fects try  to  make  a  better  one.  Thus  promote  a  healthful  ambi- 
tion to  do  good  work. 

This  is  an  outline  of  the  procedure  with  every  figure.  Only  a 
few  farther  suggestions  need  be  made. 

In  teaching  to  make  7,  first  show  the  class  seven  objects.  Let 
them  count  out  seven  counters,  or  count  seven  dots  as  you  make 
them  on  the  board.  Then  putting  the  crayon  point  on  the  board, 
have  them  tell  you  how  to  move  it  in  order  to  make  7.  They  will 
say,  "  Towards  the  door,  towards  the  clock,"  or  give  other  similar 
directions.  Lead  them  to  say,  "  To  the  right,"  "  To  the  left,"  in- 
stead. Marking  a  little  way  to  the  right,  ask, "  Which  way  now  ?  " 
Lead  them  to  notice  that  the  stem  is  just  figure  1. 


PUPILS    WHO    CANNOT  READ.  11 

Treat  4  in  the  same  way.  The  general  directions  which  the 
pupils  should  be  led  to  give  for  making  it,  are,  "  Mark  down — 
to  the  right — make  a  stem  across  the  last  line." 

As  you  proceed  to  the  more  complicated  figures,  the  importance 
of  teaching  the  pupils  to  observe  carefully  each  peculiarity  of 
form  increases.  This  will  be  best  done  by  making  the  figure 
wrong  in  various  ways,  and  telling  them  to  correct,  either  by  tell- 
ing or  by  making  a  better  one.  Thus,  make  f  instead  of  4.  Make 
n ,  or  1+ ,  or  4 ,  etc. 

Much  ingenuity  will  be  needed  in  helping  the  children  to  child- 
like descriptions  of  the  forms  of  the  various  figures.  But  be  sure 
and  let  them  tell,  in  their  own  way,  what  the  shape  is,  as  far  as 
they  can.  Their  methods  will  often  give  you  valuable  hints. 

Making  6,  9,  and  2,  will  constitute  a  second  Class  Exercise. 

The  stem  of  the  6  is  bent  (curved)  to  the  left.  Its  back  is  bent. 
It  turns  up  at  the  bottom  into  a  little  o  at  the  right.  It  has  a  kind 
of  mouth  opening  to  the  right,  etc.  (Children  are  fond  of  such 
conceits.) 

Figure  9  is  an  o  with  a  one  for  a  stem.  The  stem  is  on  the 
right.  The  o  is  at  the  top  of  the  stem  and  on  its  left. 

When  the  little  ones  attempt  to  make  these  characters  for  them- 
selves, either  on  the  board  or  on  their  slates,  you  will  often  have 
to  take  hold  of  their  hands  and  guide  them.  Manage  the  exercises 
so  as  to  give  each  one  a  great  deal  o'f  practice.  The  purpose  is 
not  to  teach  how  to  make  the  figures,  but  to  teach  the  pupils  to 
make  them  ;  and  this  can  be  accomplished  only  by  much  practice. 

Have  the  slates  brought  to  the  Counting  Table  frequently,  for  a 
class  exercise,  and  require  the  pupils  to  make  the  figures  on  their 
slates,  as  you  make  them  on  the  board. 

Figure  2  may  be  described  as  a  hook,  ?,  with  a  foot  to  it,  2 
—the  foot  running  out  to  the  right.  The  hook  bends  over  to  the 
left. 

Making  3,  5,  and  8,  will  constitute  a  third  Class  Exercise. 

Figure  3  may  be  described  as  having  two  mouths  opening  to 
the  left,  or  as  two  half  o's  one  on  top  of  the  other.  It  has  a  very 
crooked  back.  Its  back  is  at  the  right,  etc. 

Figure  5  may  be  described  as  having  a  short  stem,  a  hook  or 


12 


EXERCISES   IN   NUMBERS   FOR 


*7  *y  *7  *7  /X  *7 


666666 


half  o,  or  moutli  opening  to  the  left,  and  a  handle  or  arm  run- 
ning out  to  the  right  from  the  bottom  of  the  stem,  etc. 

The  8  is  an  S  with  a  mark  running  up  through  it. 

The  true  child's-teacher  is  fruitful  in  such  comparisons. 

Seat   Exercises. — Mark  off  on  the  blackboard  a  representation 

of  a  slate,  and  put  upon  it  a  row  of 
1's.  Let  the  pupils  make  a  similar 
row  on  their  slates.  Then  put  a  row 
of  7's  on  the  picture  of  a  slate,  and 
let  the  pupils  make  them  on  their 
slates.  Let  them  make  several  rows 
of  7's.  Then  rows  of  4's,  etc.  This 
will  constitute  an  exercise  in  copying 
figures,  and  will  need  to  be  continued 
for  several  days. 

Another  Seat  Exercise  may  be  given 
thus :  Having  no  figures  on  the  board, 
tell  the  class  to  make  a  row  of  4's,  of 
2's,  of  3's,  etc.  This  is  an  exercise  in 
remembering  the  forms  of  the  figures 

so  distinctly  as  to  be  able  to  make  them.      It  will  take  several 
exercises. 

Still  another  variety  of  Seat  Exercise  may  be  given  by  present- 
ing objects,  marks,  dots,  letters  on  the  board,  or  holding  up  fin- 
gers, and  telling  them  to  make  the  figure  which  means  so  many. 

Let  them  open  their  books  to  the  pictures  on  pages  5,  8,  and 
bid  them  make  the  figure  which  tells  how  many  kittens  there  are. 
"  Make  it  five  times."  "  Make  the  figure  which  tells  how  many 
hats  there  are."  "  Make  it  seven  times." 

Caution.  — Do  not  attempt  to  teach  them  to  make  anything 
but  the  simplest  forms  of  figures.  When  they  are  older,  and  have 
learned  to  write,  they  will  modify  the  style  somewhat  ;  but  no  one 
makes  the  more  elaborate  forms  in  common  work  on  the  slate  or 
blackboard. 


PUPILS    WHO    CANNOT  READ.  13 


LESSON    IV. 

.—^  teach  to  Count  from  Ten  to  Nine- 


teen* 

[A  review  of  preceding  lessons  is  always  to  be  woven  into  a  new  lesson.    Not 
frequent,  but  CONSTANT,  reviews,  is  what  we  need.] 

Method.  —  To  accomplish  this  purpose  will  require  several 
days,  with  several  exercises  each  day.  The  first  class  exercise 
will  begin  the  work  of  teaching  to  count  from  ten  to  fifteen.  Move 
out  the  counters  one  by  one  while  the  pupils  count  till  you  have 
moved  out  ten.  Now,  putting  another  with  these,  ask,  "  How 
many  have  we  now  ?  "  Of  course,  none  are  expected  to  know.  But 
arouse  their  curiosity,  create  a  desire  to  know,  and  then  tell  them, 
"  eleven"  (not  "leven").  So  proceed  to  fifteen.  Go  slowly.  Re- 
peat each  step  several  times. 

The  Numeral  Frame  is  exceedingly  convenient  for  this  purpose. 
Sliding  all  the  balls  to  one  side  of  the  frame,  move  all  on  the  top 
wire  to  the  other  side.  Call  attention  to  the  fact  that  there  are 
ten  in  this  row.  Then,  moving  out  one  on  the  next  wire,  then  two, 
then  three,  etc.,  and  requiring  the  pupils  to  observe,  as  you  do  so, 
the  composition  of  these  numbers  is  clearly  illustrated  to  the  eye. 

Let  the  class  name  in  concert  the  numbers  in  order  from  ten  to 
fifteen,  while  you  beat  with  the  hand.  Class  beat  and  count.  Call 
on  individuals  to  count  while  you  beat. 

Again,  use  the  counters.  Have  individuals  move  them  out  and 
count,  while  the  class  watches  to  see  if  it  is  done  right. 

Use  the  pictures  at  the  close  of  this  lesson.  Let  the  pupils 
open  their  books  to  it.  "  How  many  can  find  the  nest  ?  "  "  How 
many  eggs  are  there  in  it  ?  "  "  How  many  by  the  side  of  the 
nest?"  "  How  many  in  all?"  "Ten  and  one  are  called  what?" 
"  How  many  fishes  up  in  the  water  in  the  vase  ?  "  "  How  many 
on  the  bottom  ?  "  "  Ten  and  four  are  called  what  ?  "  etc.,  etc. 

When  they  can  count  to  fifteen,  call  their  attention  to  the  fact 


14 


EXERCISES  IN  NUMBERS  FOR 


that  we  count  from  twelve  by  saying  "  thir-teen,"  which,  means 
three  and  ten  (or  three-teen) ;  "four-teen,"  or  four-and-ten,  the  teen 
meaning  and-ten ;  fif-teen,  or  /^-and-ten,  etc.  Then  by  means 
of  the  counters  show  them  that  thir-teen  is  three-and-ten,  four-teen 
is  four-and-ten ,  etc.  Do  not  go  beyond  fifteen  until  this  idea  is 
clearly  perceived  by  all.  Use  the  subsequent  numbers,  sixteen  to 
nineteen,  as  tests.  Thus,  if  they  have  comprehended  the  idea, 
they  will  be  able  to  tell  you  what  six-and-ten  is  called,  what  seven- 
and-ten,  etc.  To  test  the  members  of  the  class  separately  use  the 
pictures  below.  Repeat  the  numbers  in  concert. 

You  will  very  naturally  speak  of  these  numbers  as  "the  teens." 
There  is  no  impropriety  in  it,  and  it  will  help  to  fix  them,  as  a 
class,  in  the  pupils'  minds. 

Seat  Exercises.—"  Each  make  eleven  figure  2's."  After  awhile, 
"Each  make  twelve  dots."  Again,  having  given  time  for  the 
former,  "  Each  make  thirteen  1's,"  etc.  These  directions  are  to 
be  given  without  interfering  with  your  other  duties,  in  a  quiet 
manner  and  low  tone,  addressed  to  the  "  C  "  class  in  their  seats. 

Be  sure  and  inspect  their  work. 


PUPILS    WHO    CANNOT   READ.  15 


LESSON    V. 

Purpose.—  .7*0  teach  to  Write  the  Numbers  from 
Ten  to  Nineteen. 

Method.—  Class  Exercise.—  Make  0  on  the  board,  telling  the 
class  its  name,  Cipher,  or  Zero.  Show  them  the  difference  between 
the  form  of  0  and  o. 

Having  taught  the  form  and  name  of  this  character  (you  need 
say  nothing  of  its  meaning,  or  use),  let  the  class  count  while  you 
make  ten  marks  on  the  board,  thus,  1  1  1  1  1  1  I  1  1  1.  Write  10 
over  the  marks,  and  tell  them  that  these  figures,  so  written,  mean 
ten.  Then,  pointing  to  the  figures,  ask,  "  What  do  1  and  0  mean 
when  written  so  ?  "  "  How  is  ten  written  in  figures  ?  "  Write 
the  0  over  the  1,  under  it,  on  the  left  of  it,  and  ask  in  each  case, 
"  Is  this  ten  ?  "  "  What  figures  do  mean  ten  ?  "  "  How  written  ?  " 
"  John,  step  to  the  board  and  write  the  figures  which  mean  ten." 
"Mary,  write  them."  "  James,"  etc.  Proceed  in  a  similar  man- 
ner to  teach  that  11  means  eleven  ;  12,  twelve  ;  13,  thirteen. 

When  they  have  gone  thus  far,  call  attention  to  the  fact  that 
you  are  just  writing  the  figures  1,  2,  3,  4,  5,  etc.,  in  order,  after  1. 
Thus,  eleven  is  written  by  putting  1  after  1,  twelve  by  putting  2 
after  1,  thirteen  by  putting  3  after  1,  etc.  Illustrate  this  by  writ- 
ing on  the  blackboard,  thus  : 


So  illustrate  and  impress  the  principle,  that  the  pupils  can  go  on 
from  13  to  19.  Such  questions  as  this  will  aid  in  this  work: 
"  What  is  the  first  figure  in  writing  each  of  the  teens  f  "  "  Well, 
then,  what  shall  I  write  first  if  I  wish  to  write  seventeen  ?  "  Get 
the  answer  from  each  pupil.  "  What  number  am  I  to  write  ?  " 
(Seven-teen.}  "What  teen?"  (Seven.)  "What,  then,  shall  I 
write  after  the  1  ?  " 


16  EXERCISES   IN  NUMBERS   FOR 

To  enliven  the  class,  call  on  Mary  to  take  up  a  handful  of  coun- 
ters and  lay  them  in  a  pile.  Let  Jane  count  them,  and  Henry 
write  the  number  on  the  board.  Sarah  add  a  handful  to  Mary's. 
James  count  this  pile.  John  write  the  number,  etc. 

Still  another  useful  exercise  will  be  secured  by  writing  the 
numbers  from  1  to  19  on  the  board,  thus  : 


0"  :  /''&''*'£&'  '"6    '?  •  f  -.f 


and  then,  as  you  point  to  them,  promiscuously,  let  the  pupils  tell 
what  they  mean.  Make  this  also  an  individual  exercise.  Name 
different  numbers  and  call  upon  pupils  to  point  to  the  figures  on 
the  board. 

For  another  exercise,  the  pupils  may  bring  their  slates  to  the 
table  and  write  the  numbers  as  you  dictate  them. 

Seat  Exercises.  —  Dictate  numbers  to  be  written  on  the  slates. 
Write  the  numbers  from  1  to  19  on  the  board  and  have  them 
copied.  Let  the  class  stand  at  the  long  board  and  write  the  num- 
bers you  name.  (Such  an  exercise  should  not  last  more  than  two 
or  three  minutes,  and  should  not  interrupt  other  duties.  Thus 
have  the  "  C  "  class  take  places  at  the  long  board  while  the  "  B  " 
or  "  A  "  class  is  coming  out  for  class  exercise.  They  should  re- 
turn, quietly,  at  a  signal,  while  other  exercises  are  going  forward.) 

Make  dots,  marks,  or  letters,  on  the  board,  and  bid  them  make 
the  figure  or  figures  which  mean  "  so  many." 

The  pictures  on  page  14  may  be  used  for  this  purpose,  by  telling 
the  pupils  to  make  the  figures  which  tell  how  many  eggs  there 
are,  when  counted  together  ;  how  many  ants,  books,  mice,  etc. 

If  the  pupils  in  their  seats  seem  restless,  have  them  stand  and 
count  in  concert.  •  They  can  count  twenty,  three  or  four  times  in  a 
minute.  They  may  have  such  an  exercise  half  a  dozen  times  a 
day. 


PUPILS    WHO    CANNOT   READ. 


17 


LESSON    VI, 

Purpose. — To  teach  the  Names  and  Meaning  of 
the  'Decades,  Twenty,  Thirty,  Forty,  etc.,  to  One 
Hundred. 


the 


are 


Method.  —  Class   Exercises.  —  "Children,  if  you  count 
thumbs  as  fingers,  how  many  fingers  has 
James  on  both  hands  ?  "     "  James,  place 
your  hands  side  by  side  on  the  table  "  (as 
in  the  margin).     "  Now,  how  many  fin- 
gers   (including    thumbs)     are     there  ? " 
"  How  many  tens  ?  "     "  Now,  James,  place 
your  hands  close  together,  and  Henry,  put 
yours  down  by  the  side  of  James's."     (See 
margin.)      "  Now,   how    many    tens 
there?"     "How  many  tens  has 
James  ?  "     "  How  many  has  Hen- 
ry ?  "     "  How  many  have  both  to- 
gether ?  "     (Two.)    "  What  do  we 
call  two  tens  ?  "    (Twenty.) 

The  accompanying  cut  may  be 
used  for  this  purpose.  All  hav- 
ing their  books  open  to  it,  ask, 
"  How  many  rails  in  this  fence  ?  " 
"  How  many  birds  on  one  of  the  top  rails  ? "  "  Count  the  birds  on 


18 


EXERCISES   IN  NUMBERS   FOR 


each  of  the  rails  ?  "  Lead  them  to  notice  that  there  are  ten  birds 
on  each  rail.  ' '  Now,  on  two  rails  there  are  how  many  tens  ?  " 
"  What  are  two  tens  called  ?  "  etc. 

Proceed  in  like  manner  to  teach  what  is  meant  by  Thirty,  Forty, 
Fifty,  etc.,  to  Ninety.  Repeat  these  names  in  concert. 

Call  attention  to  the  prefixes  Twen  (meaning  two),  Thir  (three), 
For  (four),  Fif  (five),  Six,  etc.,  and  to  the  ty  as  meaning  tens. 
Thus,  Six-ty  means  six  tens,  Seven-ty  means  seven-tens,  etc. 

Have  concert  exercises  like  this  :  "  Twenty — means  two  tens ; " 
"  TJiirty — means  three  tens  ; "  "  Forty — means  four  tens  ; "  etc. 

Again,  let  part  of  the  class  name  the  decades,  and  the  other 
part  tell  what  they  mean.  Thus,  First  Part,  in  concert,  "  Twenty  " 
—Second  Part,  "  Means  two  tens ;  "  First  Part,  "  Thirty  "—Second 
Part,  "  Means  three  tens,"  etc. 

Groups  of  dots,  or  marks  on  the  board, 
ten  in  a  group,  may  be  used  to  show  the 
meaning  of  these  terms. 

Seat  Exercises. — "  Each  make  ten  marks 
on  your  slate  and  draw  a  line  around  them, 
as  I  do  on  the  board."  "  Make  another 
ten  right  under  these,  and  draw  a  line 
around  them,  as  I  do."  So  proceed  till 
they  have  ten  groups  of  tens.  After  they 
have  made  two  or  three  groups,  the  single 
word  "  Another,"  spoken  by  the  teacher, 
will  be  sufficient  direction  to  keep  them  at 
work.  The  Numeral  Frame  may  be  used 
very  conveniently  for  this  purpose. 

These  marks  on  their  slates  may  be  made 
to  afford  an  excellent  Class  Exercise.  Thus, 
have  the  pupils  bring  their  slates  to  the 
Counting  Table.  "John,  rub  out  ten  of 
Henry's  marks."  "Henry,  rub  out  thirty 
of  your  marks."  "  Mary,  rub  out  twenty  of 
Henry's  marks."  "  Henry,  how  many 


(minim) 

(mJmm) 

(niiiiim) 


(minim) 


(/If/Ill  I IL 


f////////// 


PUPILS    WHO    CANNOT   READ.  19 

marks  have  you  now  ?  "  (This  is  not  for  the  purpose  of  teaching 
Subtraction,  but  simply  to  teach  what  twenty,  thirty,  forty,  etc., 
mean.  Do  not  ask  them  how  many  twenty  from  sixty  leaves,  or 
any  such  questions.  They  are  out  of  place  here.  Stick  to  the  sin- 
gle purpose.) 

Another  Seat  Exercise  may  be  obtained  by  having  the  ten  group? 
of  tens  made  as  before,  and  then  telling  them  to  draw  a  line 
around  twenty,  thirty,  forty,  etc. 


LESSON    VII. 


Purpose.  —  ?b  teach  to  Write  the  ^Decades,  as, 


Method.  —  Class     Exercises.—  Show   how   ten,    twenty,  a«d 

thirty  are  written,  and  then  call  attention  to  the  fact  that  0 

each  has  a  0  (zero)  at  the  right  —  that  ten  (one  ten)  has  1  at  10 

the  left  ;  twenty  (two  tens)  has  2  at  the  left  ;  and  that  thir-  20 

ty  (three  tens)  has  3  at  the  left.     Illustrate  this  by  writing  30 

the  decades  in  a  column  on  the  blackboard  as  far  as  thirty,  etc. 
and  lead  the  pupils  to  complete  the  work  on  their  slates. 

Seat  Exercises,  —  Direct  the  pupils  to  make  the  figures  which 
mean  twenty,  thirty,  forty,  etc.  Make  groups  of  ten  marks  each, 
on  the  board,  as  in  the  preceding  cut,  and  making  a  mark  around 
two,  three,  four,  or  any  number  of  them,  say,  "  Make  the  figures 
which  mean  so  many,"  etc.  Slip  three  tens  of  the  balls  on  the 
Numeral  Frame  to  one  side,  and  bid  them  make  the  figures  which 
mean  so  many.  Then  forty,  then  fifty,  etc. 

Use  the  picture  on  page  17.     "  Make  the  figures  which  tell  how 


many  birds  there  are  on  two  rails."     "  On  three,"  etc. 

. 
--»  ?••»•*  it 

UHIVE, 


*fo ' 

p 


20  EXERCISES  IN  NUMBERS  FOR 

LESSON     VIM. 

Purpose* — 2*°  teach  to  Count  through  the  ^Decades. 

Method.— Class  Exercises.  —  Have  the  pupils  count  out 
twenty  (two  tens)  of  counters,  and  place  them  by  themselves.  Put 
another  with  them,  and  lead  the  pupils  to  tell  you  that  there  are 
"  Twenty  and  one  counters."  Tell  them  that  we  call  it  "  Twenty- 
one"  instead  of  "twenty  and  one."  Put  another  counter  with 
these,  and  in  like  manner  lead  them  to  tell  you  that  there  are 
"  Twenty  and  two  counters."  Tell  them,  "  We  call  so  many, 
Twenty -two,  instead  of  twenty  and  two."  Thus  lead  them  to  count 
through  the  twenties.  Then  through  the  thirties,  etc.  They  should 
be  able  to  go  on  of  themselves  after  having  been  led  through  two 
or  three  decades.  The  Numeral  Frame  is  well  adapted  to  this 
purpose. 

There  will  be  needed  much  drill  in  repeating  in  concert  the 
names  of  the  decades,  and  in  counting  through  them.  Many  class 
exercises  will  need  to  be  devoted  mainly  to  simple  drill  in  oral 
counting  from,  one  to  one  hundred. 

Arouse  the  ambition  of  the  pupils  to  be  able  to  count  one  hun- 
dred !  Test  them  individually.  Give  them  certificates  that  they 
can  count  to  one  hundred,  when  they  can  do  it  well.  This  is  one 
of  the  greatest  mathematical  achievements  they  will  ever  make ! 
Vary  the  counting  exercise  by  having  one  count  awhile,  then 
another  go  on  a  little  further,  then  another,  etc.  Also  by  having 
them  count  around  the  class.  Thus,  beginning  at  one  end,  the 
first  pupil  says,  "  one  ;  "  the  second,  "  two  ;  "  the  third,  "  three," 
etc. ,  to  one  hundred.  This  should  be  kept  up  for  a  long  time,  till 
all  are  perfectly  familiar  with  the  order  of  the  numbers. 

Seat  Exercises. — "  Each  make  twenty  marks."  (Two  groups 
of  ten  each.)  "Make  enough  more  so  that  you  will  have  twenty- 
three  in  all."  "  Enough  more  to  make  twenty-five,"  etc.  So  of 
thirty,  forty,  etc. 


PUPILS    WHO    CANNOT  READ. 


21 


"Make  three  lines  of  marks  clear  across  your  slates"  (show 
them  how  on  the  board).  "  Count  them,  and  tell  me  how  many 
you  have." 

Use  the  picture  below.  "  How  many  birds  ?  "  "  Lambs  ?  "  etc. 
Show  from  the  picture  that  24  is  2  tens  and  4,  etc. 


LESS  ON    IX, 


.  —  ^  teach  to  Write  in  Figures  through 


the  1>ecades* 


Method. — Class  Exercises. — Let  one  pupil  count  out  ten 
counters  and  put  them  in  one  pile  on  the  counting-table,  and  have 
another  count  out  ten  more  and  place  them  in  a  pile  near  the 
former.  "  How  many  tens  have  we  here  ?  "  "  What  do  we  call 
two  tens?"  "Tell  me  how  to  write  twenty  in  figures,  on  the 
board."  "  John,  what  shall  I  write  first  ?  "  "  Jane,  what  next  ? " 


EXERCISES   IN  NUMBERS   FOR 

Now  put  the  two  piles  of  tens  together  and  lead  the  pupils  to  say 
that  there  are  twenty  in  the  pile.  Then  put  a  single  counter  near 
them,  and  ask,  "  How  many  have  we  here  in  all  ?  "  "  Twenty  and 
one  are  called  how  many  ?  "  "  What  comes  next  after  twenty  ?  " 

Then  calling  attention  to  the  20  on  the  board,  tell  them  that  the 
2,  in  the  second  place  from  the  right,  means  so  many  (two)  tens, 
and  that  whatever  stands  in  the  first  place  at  the  right  means  so 
many  more.*  Rub  out  the  0  and  put  1  in  its  place,  thus,  21. 
"  How  many  does  the  2  mean  ?  "  "  Why  does  the  two  mean  two- 
tens,  or  twenty  ?  "  (Because  it  stands  in  the  second  place  from  the 
right.)  "  What  does  this  mean  ?  "  (pointing  to  the  1.)  "  Twenty 
and  one  we  call  what  ? "  Then  write  25,  and  proceed  in  like 
manner.  Then  27,  etc.  (Do  not  use  22  until  the  idea  is  fixed. 
The  two  2's  may  trouble  them.)  Practice  upon  this  until  each 
pupil  clearly  perceives  the  principle,  and  has  it  fixed  in  the  mind. 
You  need  not  confine  yourself  to  the  twenties  in  doing  this,  nor  to 
the  numbers  in  order ;  it  will  be  better  that  you  should  not. 
Thus,  write  57.  "  What  does  the  5  mean  ?  "  (Five  tens,  or  fifty.) 
"  What  this  ?  "  (pointing  to  the  7.)  "  What  do  we  call  fifty  and 
seven  ?  "  "  Then  what  does  this  mean  ? "  (pointing  to  the  57.) 
Then  take  43,  65,  72,  or  any  of  the  numbers. 

Whether  the  fact  that  in  10,  20,  30,  40,  etc.,  the  0  is  good  for 
nothing  but  to  keep  the  place,  should  be  taught  or  not,  will  depend 
upon  the  ability  of  the  class.  I  think  it  can  usually  be  done  to 
advantage.  Thus,  write  5.  "  What  does  this  mean  ?  "  Put  0  by 
the  right  side  ofjt.  "  What  does  the  5  mean  now?"  Show  them 
that  the  0  helps  the  5  to  mean  fifty,  by  showing  that  it  is  in  the 
second  place.  It  does  nothing  else.  Now  write  5  again.  "What 
does  this  mean  ?  "  (Five.)  Put  3  at  its  right ;  thus,  53.  "  What 
does  the  5  mean  now  ?  "  "  What  helps  it  to  mean  fifty  ?  "  "  Does 
the  3  do  anything  but  help  the  5?"  It  does  something  by 
itself.  It  means  three.  In  this  manner  teach  that  0  only  serves  to 
keep  the  place,  and  show  that  the  other  figure  is  in  the  second 
place,  while  any  other  figure  will  keep  the  place  and  do  some- 
thing else. 

*  This  form  of  speech  Is  given  as  that  which  the  teacher  will  naturally  use, 
and  which  she  will  make  clear  by  her  manner. 


PUPILS    WHO    CANNOT  READ.  23 

If  these  principles  have  been  properly  taught,  the  pupils  can 
now  tell  you  how  to  write  any  number  in  any  decade.  Test  them 
on  this  point,  as  a  means  of  determining  when  your  work  is  well 
done.  Thus,  "  I  want  to  write  forty-five."  "  How  many  1 "  (Class 
say  "forty-five.")  "How  many  tens?"  "How  many  more?" 
"  What  shall  I  write  to  mean  the  tens  ?  "  "  How  many  more  do  I 
want  to  write  ? "  "  Where  shall  I  write  the  4  ? "  etc.  This  drill 
must  be  kept  up  exercise  after  exercise,  day  after  day,  till  all  can 
write  any  number  up  to  99,  readily. 

Illustrate  the  writing  of  numbers  through  the  decades  by  writ- 
ing them  on  the  board  in  this  form : 

0123456789 
10  11  12  13  14  15  16  17  18  19 
20  21  22  23  24  25  26  27  28  29 
30  31  32  33  34,  etc. 

Let  the  pupils  copy  this  arrangement  and  carry  it  forward  to 
99.  Drill  them  in  reading  the  numbers  across  the  page,  and  also 
down  the  columns. 

The  single  statement  that  100  means  ten  tens,  or  one  hundred, 
will  be  enough  on  this  point,  if  it  is  illustrated  and  dwelt  upon  till 
the  pupils  know  it. 

Seat  Exercises. — These  will  be  easily  devised.  "Each  write 
twenty-six."  "Each  write  fifty-seven."  (They  will  understand 
what  is  meant  without  saying  "the  figures  which  mean,"  etc. 
although  this  full  form  of  expression  should  be  kept  up  till  the 
thought  conveyed  is  fixed  in  mind.) 

"  Write  fifty-eight  three  times."  "  Write  sixty-three."  "  Write 
seventy-one  under  the  sixty-three,"  etc.,  etc. 

Use  the  pictures,  having  the  pupils  count  the  various  objects, 
and  write  the  number  in  figures.  Thus,  on  page  14,  "  Count  the 
fishes,  the  ants,  and  the  lilies  of  the  valley,  and  write  the  num- 
ber." Such  a  demand  as  this  will  require  several  minutes  for  its 
execution,  and  you  should  by  no  means  fail  to  examine  the  results. 
Do  not  forget  that  it  is  a  great  work  for  the  little  ones. 


24          EXERCISES  IN  NUMBERS  FOR 

Now  have  an  exercise  in  "  finding  the  page  "  in  their  books. 
"  All  turn  to  page  thirty-seven."  Require  them  to  hold  up  their 
books  so  that  you  can  see  from  your  desk  that  they  have  found 
the  right  page.  "All  find  page  fifty -three."  "Show  it  to  me," 
etc.,  etc.  Drill  on  this  till  all  can  turn  quickly  to  any  page  you 
may  name. 


LESSON    X. 

Purpose.  —  2o  teach  the  Ordinals,  or  how  to 
Number. 

Method.  —  This  may  be  done  by  having  the  class  number 
around.  Thus,  one  at  one  end  says  "  first  ;  "  the  next,  "  second  ;  " 
the  next,  "  third,"  etc. 

It  will  not  be  best  to  make  this  an  entire  exercise,  but  spend  a 
little  time  upon  it,  and  the  rest  of  the  time  on  review  exercises  in 
counting,  writing,  and  recognizing  numbers. 

Make  figures  thus  on  the  board,  beginning  at  the  right, 


"  Which  figure  did  I  make  first  ?"    "  Whi  ch,  second  ?"    "  Which, 
third,"  etc. 

Let  it  be  understood  that  you  expect  them  to  number  from  the 
right,  and  then  ask,  "  What  is  the  fourth  figure?"  "  What  the 
seventh  f  "  etc. 

Seat  Exercise.—  "  Find  the  twenty-first  page."  "The  seven- 
teenth," etc. 

This  lesson  will  require  several  days,  and  but  few  of  the  ordi- 
nals should  be  attempted  at  a  time.  Perhaps  for  the  first  exercise 
from  "first  "to  "tenth." 

It  is  not  imperative  that  the  numbering  should  be  carried  to  one 
hundredth,  al  present  ;  perhaps  to  thirtieth,  will  be  far  enough 
before  going  on  to  other  lessons.  But  if  they  see  clearly  the  prin- 
ciple they  may  ba  able  to  go  to  one  hundredth  without  difficulty. 


SECTION   II. 

ADDITION. 


LESSON    I, 

Class   Exercises, 

Purpose. — To   teach  how  to  find  out  the  sum  of 
any  two  numbers  between  one  and  nine. 


*  This  lesson  is  not,  strictly  speaking,  a  lesson  in  Addition  ;  — it 
is  a  lesson  in  Counting,  and  is  preparatory  to  Addition.  Addition 
and  counting  are  not  the  same  thing.  The  arithmetical  process 
which  we  call  Addition  is  a  method  of  finding  the  sum  of  numbers 
by  means  of  a  knowledge  of  the  sums  of  the  digits  two  and  two, 
i.  e.,  by  means  of  a  knowledge  of  the  Addition  Table.  Hence,  as 
preparatory  to  Addition,  the  pupil  needs — 


*  The  paragraphs  in  small  type  are  exclusively  for  the  Teacher's  use.    Those 
in  the  larger  type  are  for  the  children  to  study  at  their  seats. 


26  ADDITION.— EXERCISE  S   FOR 

1.  To  learn  to  make  the  Addition  Table;  and 

2.  To  commit  this  table  to  memory. 

Having  done  this  he  is  ready  to  learn  Addition  proper. 

The  only  way  in  which  the  pupil  can  find  out,  in  the  first  in- 
stance, what  is  the  sum  of  any  two  numbers,  as  4  and  5,  is  by  tak- 
ing one  number  and  counting  on  the  other.  But  this  is  not  addi- 
tion. When  the  pupil  has  in  this  way  learned  the  meaning  of  the 
Addition  Table,  and  can  make  it  readily,  he  is  prepared  to  commit 
it  to  memory.  This  is  the  second  step  :  and  not  until  the  table  is 
thoroughly  learned,  is  the  pupil  prepared  to  enter  upon  Addition. 
It  is  just  at  this  point  that  all  the  difficulty  in  teaching  Addition 
occurs.  The  pupil  is  allowed  to  attempt  adding  before  he  is  fa- 
miliar with  this  table  ;  hence  he  necessarily  falls  into  the  habit  of 
counting.  But  if  he  is  not  allowed  to  enter  upon  Addition  proper 
(Lesson  III.)  until  he  can  tell  with  perfect  ease  the  sum  of  any  two 
digits,  at  sight,  there  will  be  no  trouble  arising  from  a  propensity 
to  count.  This  propensity  arises  solely  from  an  imperfect  knowl- 
edge of  the  Addition  Table. 

We  now  proceed  to  exhibit  in  detail  some  methods  of  conduct- 
ing class  exercises  for  the  purpose  designated  at  the  head  of  this 
lesson. 

Have  the  class  count  while  you  place  four  counters  in  one  pile, 
and  three  counters  in  another  pile  near  the  first.  "  How  many 
are  there  in  this  pile  ? "  (pointing  to  the  four.}  "  How  many  in 
this?"  (pointing  to  the  three.}  "Now,  who  can  tell  how  many 
there  are  in  both  piles  ?  "  Of  course  it  is  not  expected  that  any 
one  can.  But  arouse  the  desire  to  find  out.  Then  show  them 
how,  by  beginning  with  the  four,  and  counting  on  the  three, 
they  can  find  out  how  many  there  are  in  both  piles.  Thus, 
ask,  "  How  many  are  there  here  ?  "  (pointing  to  the  four.)  Move 
one  of  the  three  up  to  the  four.  "  How  many  now  ? "  Move  up 
another.  "  How  many  now  ?  "  The  other.  "  How  many  now  ?  " 
"  Now  we  have  put  the  three  with  the  four."  "  How  many  are 
four  and  three  together  ?  " 

Again,  place  5  in  one  pile  and  6  in  anoth- 
er, and  teach  them  how  to  find  out,~by  count- 
ing, how  many  5  and  6  put  together  make. 


PUPILS  READING  SIMPLE    WORDS.     27 

Also  lead  them  to  determine  how  many  5  and  6  make  by  placing 
the  counters  in  each  collection  so  that  they  can  be  counted  with- 
out being  moved. 

The  Numeral  Frame  may  also  be  used  for  our  present  purpose. 
Thus,  holding  it  up  before  the  class,  let  the  pupils  count  out  5 
balls  as  you  move  them  to  one  side  on  the  upper  wire.  Then 
count  out  4  on  the  second  wire,  moving  them,  under  the  five. 
"  How  many  balls  have  we  here  ?  "  (pointing  to  the  5.)  "  How 
many  have  we  here  ?  "  (pointing  to  the  4.)  "  How  many  in  all  ?  " 
"  How  many  are  5  and  4  ?  " 

Again,  propose  the  question,  "  How  many  are  5  and  3  ? "  and  let 
the  pupils  work  out  the  answer  by  moving  the  balls.  So,  also,  ad- 
dress such  questions  as  the  following  to  individuals,  and  let  them 
find  out  the  answers  by  moving  the  balls  :  "  How  many  are  4  and 
2  ?  "  "  How  many  are  7  and  3  ? "  etc. 

Counting  ly  2's,  3's,  4's,  etc.,  is  a  very  useful  exercise  for  many 
purposes,  especially  as  it  furnishes  such  a  variety  of  systematic 
exercises  in  a  convenient  form  for  drill.  But  let  the  exercise  be 
restricted  to  the  single  purpose  had  in  view  at  the  time  :  our  pres- 
ent object  is  to  teach  to  make  the  Addition  Table.  For  this  purpose, 
as  well  as  for  the  purpose  of  fixing  the  table  in  memory,  it  is  not 
legitimate  to  carry  this  form  of  counting  beyond  those  steps 
which  require  the  combination  of  single  digits ;  for  example,  in 
counting  by  2's  we  shall  have  these  combinations,  2,  4,  6,  8,  10  ; 
1,  3,  5,  7,  9,  11 ;  and  no  more.  Counting  by  3's  we  shall  have 
3,  6,  9,  12 ;  1,  4,  7,  10 ;  2,  5,  8,  11  ;  and  no  more.  After  the  pupils 
comprehend  the  order,  these  combinations  can  be  assigned  as  seat 
exercises  ;  for  example,  tell  them  to  write  on  their  slates  the  num- 
bers as  they  count  by  4,  first  beginning  with  1.  These  results  will 
be  written  thus : 

/,    <,    ?,     /*. 

Again  count  by  4's  beginning  with  2,  and  write  the  results.    These 
will  be  2,  6, 10. 

The  several  exercises  thus  outlined  will  be  distributed  through 
a  number  of  days,  only  one  Icing  used  at  a  time,  and  this  repeated 
till  it  is  familiar  before  passing  to  another. 


28 


ADDITION.— EXERC2 SES   FOR 


Do  not  attempt,  at  this  time,  to  have  them  remember  how  many 
any  combination  makes.  The  present  purpose  is  merely  to  learn 
how  to  find  out  what  4  and  3,  5  and  6,  etc.,  make.  In  this  first  ex- 
ercise do  not  take  either  the  smallest  or  the  largest  numbers. 

Give  them  sufficient  practice  so  that  they  can  study  the  follow- 
ing seat  exercise.  Write  the  figures  4,  3,  5,  2,  1  on  the  board,  with 
the  corresponding  words  printed  under  them,  thus, 


3     / 


Four.       Three. 


Five. 


Two. 


One. 


If  the  pupils  do  not  know  all  these  words,  they  should  be  taught 
them,  or  at  least  be  shown  how  to  find  out  what  they  are  by  look- 
ing at  the  board. 


Seat  Exercise. 


1.  How  many  birds  are  on 
the  box  ? 

2.  How  many  birds  are  in 
the  tree  ? 

3.  How  many  birds  in  all  ? 

4.  How  many  birds  are 
four  birds  and  three  birds  ? 


5.  How  many  birds  are  on  the 
barn? 

6.  How  many  birds  are  flying  to 
the  barn  ? 

7.  How  many  birds  in  all  ? 

8.  How   many  birds    are  five 
birds  and  three  birds  ? 


PUPILSREADING   SIMPLE    WORDS.       29 


9.  How  many  cats  are  on  the 
table  ? 

10.  How  many  cats  are  on  the 
floor  by  the  table  ? 

11.  How  many  cats  in  all  ? 

12.  How  many  cats  are  three 
cats  and  three  cats  ? 

13.  How  many  boys 
are  at  play  under  the 
tree? 

14.  How  many  girls 
are  at  play  under  the 
tree  ? 

15.  How  many  boys 
and  girls  in  all  ? 

16.  How  many  are 
2  boys  and  3  girls? 

17.  How    many    caps    are    hung 
up? 

18.  How  many  caps  are  on  the 
floor  ? 

19.  How  many  caps  are  there  in 

all? 

20.  How  many  caps  are   4  caps 

and  2  caps  ? 


Recitation  and  Class  Exercise. 

We  are  now  to  have  our  first  Recitation. 

With  books  in  hand,  let  the  pupils  read  the  questions  in  the 
preceding  Seat  Exercise,  and  give  the  answers.     They  are  not  ex- 


30  ADDITION.— EXERCISES   FOR 

pected  to  have  learned  the  combinations,  as  how  many  4  and  3 
make,  but  only  how  to  find  out  ly  counting,  as  above  explained. 
Give  time  to  do  this  in  the  recitation.  To  give  variety,  let  one 
read  a  question  and  another  answer  it.  But,  do  not  go  round  in 
order.  Say,  "All  read  the  first  question,  silently."  Give  time. 
"Jane,  read  it  aloud."  "  John,  answer  it."  Thus,  letting  no  one 
know  who  is  to  read,  or  who  is  to  answer,  keep  all  in  readiness. 

When  they  have  had  a  fair  opportunity  to  show  that  they 
studied  the  lesson  well,  give  them  a  new  exercise. 

Give  them  sufficient  practice  to  enable  them  to  find  out  the  an- 
swers  to  the  following,  while  in  their  seats,  and  write  the  answers 
in  order  on  their  slates,  while  in  their  seats. 


Seat  Exercise. 


1.  How  many  are  4  and  3  ? 

2.  How  many  are  3  and  6  ? 

3.  How  many  are  2  and  3  ? 

4.  How  many  are  5  and  1  ? 

5.  How  many  are  4  and  1  ? 

6.  How  many  are  3  and  1  ? 

7.  How  many  are  2  and  7  ? 

8.  How  many  are  6  and  8  ? 


9.  How  many  are  7  and  6  ? 

10.  How  many  are  8  and  5  ? 

11.  How  many  are  6  and  1  ? 

12.  How  many  are  9  and  2  ? 

13.  How  many  are  8  and  3  ? 

14.  How  many  are  7  and  9  ? 

15.  How  many  are  6  and  7  ? 

16.  How  many  are  7  and  8  ? 


Recitation  and   Class   Exercise. 

First,  the  pupils  having  brought  their  books,  and  their  slates 
with  the  answers  in  order  on  them,  read  the  questions  to  them, 
and  let  them  give  the  answers  as  they  have  them  on  their  slates. 
Let  several  pupils  give  the  answer  which  they  have  to  each  prob- 
lem, as  it  is  called  for.  If  they  do  not  agree,  have  the  class  find 
out  which  is  right.  It  may  take  several  exercises  to  get  them  all 
to  write  their  answers  in  good  order  on  their  slates  ;  but  the  effort 
should  be  repeated  and  persisted  in  until  they  do  it. 

Second,  having  gone  through  with  all  the  questions,  and  given 
all  the  pupils  a  full  opportunity  to  exhibit  their  work,  give  a  new 


PUPILS  READING   SIMPLE    WORDS.      31 

exercise.  Let  this  be  to  teach  them  how  to  use  marks  like  /  /  /  /, 
and  the  balls  on  the  Numeral  Frame,  for  the  purpose  of  finding 
out  what  the  sum  of  two  numbers  is.  (See  page  27.) 

The  following  exercise  is  to  be  studied  by  the  pupils  in  their 
seats,  and  the  answers  written  in  order  on  their  slates  in  the  same 
manner  as  the  last. 


Seat  Exercise. 


1.  How  many  are  5  and  9  ? 
2.  How  many  are  6  and  1  ? 
3.  How  many  are  7  and  4  ? 
4.  How  many  are  4  and  9  ? 
5.  How  many  are  5  and  2  ? 
6.  How  many  are  8  and  9  ? 
7.  How  many  are  3  and  7  ? 

8.  How  many  are  2  and  9  ? 
9.  How  many  are  1  and  1  ? 
10.  How  many  are  2  and  1  ? 
11.  How  many  are  5  and  6  ? 
12.  How  many  are  8  and  7  ? 
13.  How  many  are  3  and  9  ? 
14.  How  many  are  1  and  8  ? 

Recitation  and  Class  Exercise. 

The  recitation  will  be  similar  to  the  last,  the  design  being  to 
satisfy  yourself  that  the  pupils  have  done  the  work  well,  which 


32 


ADDITION.— EXERCISES  FOR 


was  assigned  them  to  do  in  their  seats,  and  to  make  them  feel  that 
you  notice  and  appreciate  their  efforts. 

For  a  New  Class  Exercise  teach  them  that  +  means  the  same  as 
"and,"  and  =,  the  same  as  "make,"  or  "are."  Write  on  the 
board  4  +  5  =  9,  6  +  4  =  10,  and  similar  expressions,  and  teach 
them  to  read  them  '  '4  and  5  are  9,"  "  6  and  4  are  10,"  etc.  Then 
give  them  what  instruction  they  may  need  to  enable  them  to  copy 
the  next  seat  exercises  upon  their  slates,  and  to  determine  the  an- 
swers by  counting,  with  or  without  objects,  and  to  fill  out  the  ex- 
pressions. 


Seat  Exercise. 


6  +  4  = 

7  +  1  = 
5  +  6  = 


8  +  9  = 

7  +  4  = 

3  +  7 

7  +  6  = 

6  +  9  = 

0  +  0 

3  +  1  = 

8  +  8  = 

2  +  0 

4  +  1  = 

6  +  6  = 

3  +  5 

8  +  3  = 

4  +  0  = 

9  +  4 

Recitation  and  Class  Exercise. 

Examine  the  pupils'  slates  to  see  that  the  work  is  done  neatly. 
Question  them  thus :  "  6  and  4  are  how  many  ? "  "7  and  6  ? " 
etc.  When  a  question  is  asked,  have  all  look  up  the  answer  on 
their  slates,  and  then  call  on  some  one  to  answer,  allowing  the 
others  to  correct  the  reply,  if  wrong. 

For  a  new  exercise,  show  them  how  to  make  the  Addition  Table, 
as  indicated  in  the  following  exercise.  Their  slates  are  to  be 
ruled,  and  the  table  copied  and  filled  out. 

Let  it  be  borne  in  mind  that  it  is  ability  to  find  out  by  counting, 
what  the  sum  of  any  two  numbers  each  expressed  by  a  single 
figure  is,  that  we  are  seeking  to  secure.  We  are  not  now  requir- 
ing the  pupils  to  memorize,  but  to  make  the  Addition  Table. 
swers  by  counting,  with  or  without  objects,  and  to  fill  out  the  ex- 
pressions, 


PUPILS  READING   SIMPLE 


Seat  Exercise. 


iroRDS.     33 


1  +  1  = 

1  +  2  = 

1+3  = 

2  +  1  = 

2  +  2  = 

2  +  3  = 

3  +  1  = 

3  +  2  = 

3  +  3  = 

4  +  1  = 

4  +  2  = 

5  +  1  = 

5  +  2  = 

6  +  1  = 

6  +  2  = 

7  +  1  = 

7  +  2  = 

8  +  1  = 

8  +  2  = 

9  +  1  = 

9  +  2  = 

1  +  4  = 

1  +  5  = 

1  +  6  = 

2  +  4  = 

2  +  5  = 

2  +  6  = 

3+4  = 

3 

4 

5 

6 

7 

8 

9 

1  +  7  = 

1  +  8  = 

1  +  9  = 

o 

3 


02 


+3 

(=! 

0) 


0) 


o 

03 


a  « 

•fi 

l-H       .2 


N  - 
'S      fafl 

O     G 

a  -3 

o  'd 

a  » 

_0  03 


g  ft 

IS 

TJ 

5 


S 


f     o5 

03      « 

S«iH 
2 
o  d 


34  ADDITION.— EXERCISES   FOR 


Recitation  and  Class  Exercise. 

Making  the  above  table  will  afford  three  or  more  seat  exercises. 
Each  part  should  be  made  several  times  over,  until  all  can  be 
made  with  ease.  The  class  exercises  will  be  similar  to  that  sug- 
gested last.  Remember  that  the  present  purpose  is  to  learn  how 
to  find  out  what  these  combinations  are.  The  next  lesson  will  be 
devoted  to  fixing  them  in  memory. 

A  good  class  exercise  can  be  obtained  by  writing  a  series  of 
combinations  on  the  board,  thus  : 


1  +  5  = 

6  +  3  = 
8  +  5  = 
etc.  ; 

and  as  you  point  to  any  combination,  let  the  pupils  raise  their 
hands  as  soon  as  they  can  tell  what  it  makes.  Then  call  on  indi- 
viduals to  answer. 


Seat  Exercise. 

1.  A  boy  has  three  apples  and  a  girl  gives  him  five 
more.     How  many  has  he  then  ? 

2.  Frank  has  2  tops  and  George  has  3.    How  many 
have  they  both  ? 

3.  There  are  3  birds  on  one  tree  and  8  birds  on  another. 
How  many  birds  are  there  on  both  trees  ? 

4.  Ann  has  seven  flowers  and  George  gives  her  six 
more.     How  many  has  she  then  ? 


PUPILS  READING  SIMPLE    WORDS.      35 

5.  There  are  5  books  on  the 
chair  and  8  on  the  table.  How 
many  books  are  there  in  all  ? 

G.  There  are  4  chickens  in 
the  barn  and  7  in  the  yard. 
How  many  chickens  are  there 
in  all  ? 

7.  There  are  5  eggs  in  one 
nest  and  7  in  the  other.    How 
many  eggs  in  both  nests  ? 

8.  If  the  black  cat  has  four 
kittens  and  the  white  cat  has 
six,  how  many  kittens  have  both  ? 

9.  How  many  letters  are  there  in  the  word  ground  ? 
How  many  in  the  word  white  ?     How  many  in  both 
words  ?     How  many  are  six  and  five  ? 

10.  How  many  letters  are  there  in  the  word  teacher  ? 
How  many  in  the  word  boy  ?   How  many  in  both  words  ? 
How  many  are  7  and  3  ? 

[See  first  Recitation  and  Class  Exercise  for  method  in  this  case.] 


LESSON    II. 

.—  ^  fix  the  Addition  Table  in  the  mem- 
ory, so  that  the  pupil  can  tell  the  sum  of  any  two 
numbers  between  /  and  9  with  readiness. 

Class   Exercise. 

Show  them,  by  the  use  of  the  counters  or  other  objects,  that  3 
and  2  are  the  same  as  2  and  3  ;  5  and  4,  as  4  and  5,  etc. 

"  If  you  have  three  nuts  in  your  left  hand  and  5  in  your  right, 


36 


ADDITION.— EXERCISES   FOR 


how  many  nuts  have  you  in  all  ?  "  "  If  you  change  and  take  5  in 
your  left  hand  and  3  in  your  right,  how  many  have  you  then  ?  " 
"  3  and  5  are  the  same  as  what  ? " 

Be  sure  that  this  is  understood  and  fixed  in  mind.  It  diminishes 
the  work  of  learning  the  addition  table  one-half. 

When  this  principle  is  well  learned,  drill  them  in  concert  on  the 
1's  of  the  Addition  Table.  Thus,  have  them  all  say,  "  1  and  1  are 
2,"  "  2  and  1  are  3,"  "  3  and  1  are  4,"  etc. 

Again,  write  on  the  board  such  examples  as  these  : 


1        1 
3       5 


1 
4 


1 
1 


1  1 

2  6 


6 
1 


1 

7 


7 
1 


1 

8 


8 
1 


Then,  as  you  point  to  the  example,  ask,  "  How  many  are  3  and 
1  ? "  Tell  them,  "  We  will  write  the  answer  right  under  the 
line."  Having  done  it,  proceed  in  like  manner  with  the  rest. 

Show  them  how  to  perform  the  following  exercise,  by  copying 
it  on  their  slates  and  writing  in  the  answers.  Each  of  the  nine 
following  exercises  are  to  be  thus  copied  and  filled  out,  and  the 
FIRST  COLUMN  IN  EACH  THOROUGHLY  MEMORIZED. 


Seat  Exercise. 


1  +  1  = 

2  +  1  = 

6  +  1  = 

1  + 

=    8 

2  +  1  = 

1  +  2  = 

1  +  6  = 

1  + 

=    9 

3  +  1  = 

3  +  1  = 

7  +  1  = 

1  + 

=    7 

4  +  1  = 

1  +  3  = 

1  +  7  = 

1  + 

=    6 

5  +  1  = 

4  +  1  = 

8  +  1  = 

1  + 

—    4 

6  +  1  = 

1  +  4  = 

1  +  8  = 

1  + 

=    3 

7  +  1  = 

5  +  1  = 

9  +  1  = 

1  + 

=  10 

8  +  1  = 

6  +  1  = 

1  +  9  = 

1  + 

=    2 

9  +  1  = 

1  +  0  = 

0  +  1  = 

1  + 

=    5 

1.  George  has  three  pigs  and  Frank  has  one  pig.   How 
many  pigs  have  both  ? 


PUPILSREADING    SIMPLE    WORDS.    37 


2.  Mary  has   1    chicken   and  Jane  has   7  chickens. 
How  many  chickens  have  both  ? 

3.  One  and  3  are  how  many  ? 

4.  One  and  what  make  four  ? 

5.  Three  and  what  make  four  ? 

6.  Five  and  one  are  how  many  ? 

7.  Five  and  what  make  six  ? 

8.  One  and  what  make  six  ? 

9.  Mary  has  4  flowers.     How  many  more  must  she 
get  to  have  five  ? 

10.  George  has  1  top.    How  many  more  must  he  get 
to  have  4  ? 

11213141516171819 
12131415161718191 


Recitation  and  Class  Exercise. 

First,  EXAMINE  THE  PUPILS1  WORK. 

Have  the  pupils  repeat  the  "  ones  column  "  (the  left-hand  one) 
down  and  up,  by  having  the  first  pupil  say,  "  One  and  one  are 


38 


ADDITION.— EXERCISES   FOR 


two ;"  the  second,  "  Two  and  one  are  three  ;"   and  so  on  around 
the  class.    Then  say  it  backwards  in  the  same  manner. 

Then  vary  the  exercise  by  having  one  say,  "  Nine  and  one  are 
ten  ; "  and  the  next,  "  One  and  nine  are  ten ; "  etc. 

Dictate  the  second  and  third  columns,  and  have  the  pupils  an- 
swer. Thus,  say,  ' '  1  and  2  are ? "  and  when  all  have 

thought,  name  some  one  to  answer.     So  of  the  others. 

Again,  have  the  pupils  read  the  fourth  column,  supplying  the 
answers  as  they  read. 

Give  the  necessary  instruction  to  enable  the  pupils  to  prepare 
the  next  lesson.  This  and  the  subsequent  exercises  of  this  lesson 
are  to  be  copied  on  the  slates  and  treated  as  the  last.  The  same 
general  plan  of  recitation  will  be  pursued  in  each  of  the  eight  fol- 
lowing exercises. 

In  talking  with  the  class  about  these  exercises  as  they  come  to 
them,  show  them  that  1  +  2,  in  the  2's  column,  1  +  3,  and  2  +  3, 
in  the  3's  column,  etc.,  have  been  previously  learned. 

The  teacher  needs  to  bear  in  mind  that  ability  to  add  ~by  sight  is 
quite  as  important  as  ability  to  add  by  sound,  and  adapt  the  drill 
exercises  to  the  fact.  Again,  a  fundamental  purpose  in  these  ex- 
ercises is  to  teach  the  component  parts  of  the  numbers  from  2  to  18, 
so  that  they  will  be  instantly  recognized. 


Seat  Exercise. 


1  +  2  = 

6+2  = 

2  +   =4 

2  +  2  = 

2  +  1  = 

2+6  = 

2  +  =6 

3  +  2  = 

2  +  2  = 

7  +  2  = 

2  +  =8 

4  +  2  = 

3  +  2  = 

2+7  = 

2  +  =5 

5  +  2  = 

2  +  3  = 

8+2  = 

2  +   =10 

6  +  2  = 

4  +  2  = 

2+8  = 

2  +   =10 

7  +  2  = 

2  +  4  = 

9+2  = 

2+   =3 

8  +  2  = 

5  +  2  = 

2+9  = 

2  +  =7 

9  +  2  = 

2  +  5  = 

0+2  = 

2+  =9 

PUPILS   READING    SIMPLE     WORDS.    39 


1.  Ann  has  8  flowers  and  George  has  2.     How  many 
have  both  ?     If   Ann  has  2  and  George  8,  how  many 
have  both  ? 

2.  Frank  has  2  hens  and  George  has  6.     How  many 
have  both  ?    If  Frank  has  6  and  George  2,  how  many 
have  both  ? 

3.  Two  white  pigs  and  four  black  pigs  are  how  many  ? 
Four  white  pigs  and  2  black  ones  are  how  many  ? 

4.  Two  and  three  are  how  many  ? 

5.  Two  and  what  make  five  ? 

6.  Three  and  what  make  five  ? 

7.  Eight  and  two  make  how  many  ? 

8.  Eight  and  what  make  10  ? 

9.  Two  and  what  make  10  ? 

10.  There  are  3  eggs  in  the  nest.  How 
many  more  must  the  hen  lay  to  make  5  ? 

11.  If  James  has  learned  6  words,  how 
many  more  must  he  learn  to  know  8  ? 

12223242526272829 
21232425262728292 


40 


ADDITION.— EXERCISES   FOR 


Seat  Exercise. 


1  +  3  = 

6  +  3 

3  +  1  = 

3  +  6 

3  +  3  = 

2  +  3  = 

7  +  3 

4  +  3  = 

3  +  2  = 

3  +  7 

5  +  3  = 

3  +  3  = 

8  +  3 

6  +  3  = 

4  +  3  = 

3  +  8 

7  +  3  = 

3  +  4  = 

9  +  3 

8  +  3  = 

5  +  3  = 

3  +  9 

9  +  3  = 

3  +  5  = 

0  +  3 

3  + 

=  8 

3  + 

=   9 

3  + 

=  7 

3  + 

=  11 

3  + 

=  10 

3  + 

=  12 

3  + 

=  4 

3  + 

=  5 

3  + 

=  6 

1.  George  has  7  books  and  Mary  has  3.    How  many 
have  both  ? 

2.  There  are  five  lambs 
in  one  field  and  three  in 
another.     How  many  are 
there  in  both  fields  ? 

3.  If  there  are  9  cows  in 
one  field  and  3  cows  in  an- 
other, how  many  are  there 
in  both  fields  ? 


4.  Eight  eggs  in  the  nest 
and  three  in  your  hand, 
make  how  many  eggs  ? 

5.  Four  and  three  are  how  many  ? 

6.  Three  and  what  make  seven  ? 

7.  Four  and  what  make  seven  ? 

8.  Five  and  four  are  how  many  ? 

9.  Five  and  what  make  nine  ? 

10.  Four  and  what  make  nine  ? 

11.  Four  and  eight  are  how  many  ? 


PUPILS  READING   SIMPLE    WORDS.       4] 


Seat  Exercise. 


1  +  4  = 

6  +  4 

4  +  1  = 

4  +  6 

2  +  4  = 

7  +  4 

4  +  4  = 

4  +  2  = 

4  +  7 

5  +  4  = 

3  +  4  = 

8  +  4 

6  +  4  = 

4  +  3  = 

4  +  8 

7  +  4  = 

4  +  4  = 

9  +  4 

8  +  4  = 

5  +  4  = 

4  +  9 

9  +  4  = 

4  +  5  = 

0  +  4 

4  + 

=   6 

4  + 

=  7 

4  + 

=  9 

4  + 

=  12 

4  + 

=  5 

4  + 

=  10 

4  + 

=  8 

4  + 

=  13 

4  + 

=  11 

1.  Four  girls  and  five  girls  are  how  many  girls  ? 

2.  Five  boys  and  four  boys  are  how  many  boys  ? 

3.  Nine  pigs  and  four  pigs  are  how  many  ? 

4.  There  are  7  sheep  in  one  field  and  4  in  another. 
How  many  are  there  in  both  ? 

5.  How  many  letters  are  there  in  the  word  George  ? 
How  many  in  the  word  read  ?    How  many  letters  in  both 
words  ? 

6.  George  has  4  tops.    How  many  more  must  he  get  to 
have  6  ?     How  many  to  have  9  ? 

7.  Mary  has  3  flowers.    How  many  more  must  she 

get  to  have  7  ? 

8.  Jane  has  7  chickens.     How  many  more  must  she 

get  to  have  11  ? 

9.  One  day  the  hen's  nest  had  9  eggs  in  it.     On  an- 
other day  it  had  13.    How  many  new  eggs  had  been  laid 
in  it? 


14243445464748494 
41424344546474849 


42 


ADDITION.— EXERCISES  FOR 


Seat  Exercise. 


5  +  5  = 

6  +  5  = 

7  +  5  = 

8  +  5  = 

9  +  5  = 


1  +  5  = 
5  +  1  = 

2  +  5  = 
5  +  2  = 

3  -t-5  = 
5  +  3  = 

4  +  5  = 

5  +  4  = 
5  +  5  = 


6  +  5  = 

5  +  6  = 

7  +  5  = 
5  +  7  = 

8  +  5  = 
5  +  8  = 

9  +  5  = 
5  +  9  = 
0  +  5  = 


1.  Five  and  seven  are  how 


6  + 

2  + 
8  + 

4  + 
1  + 

5  + 

3  + 

7  + 
9 


=  11 

=  7 
=  13 
=  9 
=  6 
=  10 

o 

=12 
=  14 


many  r 

2.  Five  and  what  make  12  ? 

3.  Seven  and  what  make  12  ? 

4.  Nine  and   five    are  how 
many  ? 

5.  Eight  and  what  make  13  ? 

6.  Five  and  what  make  13  ? 

7.  Five  and  what  make  14  ? 

8.  Five  and  what  make  11  ? 

9.  Five  and  what  make  10  ? 

10.  George  has  6  nuts  and  John  has  5.     How  man} 
have  both  ? 

11.  Mary  has  7  flowers.    How  many  more  must  she  get 
to  have  12  ? 

12.  Jane  has   learned  five  words.    How  many  more 
must  she  learn  to  know  10  ? 


15253545565758595 
51525354556575859 


PUPILS  READING   SIMPLE    WORDS.       43 


Seat  Exercise. 


1  +  6  = 

5  +  6 

6  +  1  = 

6  +  5 

2  +  6  = 

7  +  6 

6  +  2  = 

6  +  7 

3  +  6  = 

8  +  6 

6  +  6  = 

6  +  3  = 

6  +  8 

7  +  6  = 

4  +  6  = 

9  +  6 

8  +  6  = 

6  +  4  = 

6  +  9 

9  +  6  = 

6  +  6  = 

0  +  6 

1.  Six  and  eight  are  how  many  ? 

2.  Six  and  what  make  14  ? 

3.  Eight  and  what  make  14  ? 

4.  Six  and  seven  are  how  many  ? 

5.  Six  and  what  make  13  ? 

6.  Seven  and  what  make  13  ? 

7.  Six  and  nine  are  how  many  ? 

8.  Six  and  what  make  15  ? 

9.  Nine  and  what  make  15  ? 


6  + 

=  9 

6  + 

=  12 

6  + 

=  11 

6  + 

=  7 

6  + 

=  10 

6  + 

=  8 

6  + 

=  15 

6  + 

=  13 

6  + 

=  14 

10.  If  John  gives  Mary  eight  flowers,  how  many  must 
James  give  her  so  that  she  will  have  14  ? 


44 


ADDITION.— EXERCISES   FOR 


12.  John  gave  Mary  seven  flowers  and  James  gave  her 
six.    How  many  did  she  then  have  ? 

13.  If  John  finds  9  eggs,  how  many  must  George  find 
to  make  15  ? 

16263646566768696 
61626364656676869 


Seat  Exercise. 


1  +  7  = 

5  +  7 

7  +  1  = 

7  +  5 

2  +  7  = 

6  +  7 

7  +  2  = 

7  +  6 

3  +  7  = 

8  +  7 

7  +  3  = 

7  +  8 

7  +  7  = 

4  +  7  = 

9  +  7 

8  +  7  = 

7  +  4  = 

7  +  9 

9  +  7  = 

7  +  7  = 

0  +  7 

7  + 

=  13 

7  + 

=  8 

7  + 

=10 

7  + 

=  14 

7  + 

=  16 

7  + 

=   9 

7  + 

=  11 

7  + 

=  15 

7  + 

=  12 

1.  Eight  and  seven  are  how  many  ? 

2.  Eight  and  what  make  15  ? 

3.  Seven  and  what  make  15  ? 

4.  Nine  and  seven  are  how  many  ? 

5.  Nine  and  what  make  16  ? 

6.  Seven  and  what  make  16  ? 

7.  Seven  angl  what  make  14  ? 

8.  John  has  learned  7  words.    How  many  more  must 
he  learn  to  know  14  ? 

9.  If  Frank  and  Mary  find  15  eggs,  and  Mary  finds 
seven  of  them,  how  many  does  Frank  find  ? 


PUPILS  READING   SIMPLE    WORDS.      45 


10.  Peter  and  John  have  16  apples,  and  Peter  has  9  of 
them.     How  many  has  John  ? 


Seat  Exercise. 

1  +  8  = 
8  +  1  = 

2  +  8  = 
8  +  2  = 

3  +  8  = 
8  +  3  = 

4  +  8  = 

8  +  8=  8  +  4  = 

9  +  8=  8  +  8  = 

1.  Eight  and  eight  are  how  many  ? 

2.  Eight  and  what  make  16  ? 

3.  Eight  and  nine  are  how  many  ? 

4.  Eight  and  what  make  17  ? 

5.  Nine  and  what  make  17  ? 


5  +  8  = 

8  + 

=  14 

8  +  5  = 

8  + 

=10 

6  +  8  = 

8  + 

=  9 

8  +  6  = 

8  + 

=  12 

7  +  8  = 

8  + 

=  16 

8  +  7  = 

8  + 

=  11 

9  +  8  = 

8  + 

=  15 

8  +  9  = 

8  + 

=  13 

0  +  8  = 

8  + 

=  17 

46 


ADDITION.-EXERCI SES   FOR 


6.  If  there  are  eight  girls  and  nine  boys  in  the  yard, 
how  many  are  there  in  all  ? 

7.  If  there  are  17  children  in  the  yard  and  eight  of 
them  are  girls,  how  many  are  boys  ? 

8.  If  there  are  17  children  in  the  yard  and  nine  of 
them  are  boys,  how  many  are  girls  ? 

18283848586878898 
81828384858687889 


Seat  Exercise. 


1  +  9  = 

5  +  9  = 

9  +     =11 

9  +  1  = 

9  +  5  = 

9  +      =13 

2  +  9  = 

6  +  9  = 

9  +     =15 

9  +  2  = 

9  +  6  = 

9  +     =10 

3  +  9  = 

7  +  9  = 

9  +      =12 

9  +  3  = 

9  +  7  = 

9  +      =16 

4  +  9  = 

8  +  9  = 

9  +      =14 

9  +  4  = 

9  +  8  = 

9+     =17 

9  +  9  = 

0  +  9  = 

9  +     =18 

9  +  9  = 

1.  Nine  and  nine  are  how  many  ? 

2.  Nine  and  what  make  18  ? 

3.  How  many  nines  make  18  ? 

4.  There  are  8  red  apples  and  9  green  apples  in  a  dish. 
How  many  apples  are  there  in  the  dish  ? 

5.  There  are  17  apples  in  a  dish.     9  of  them  are  red 
and  the  others  green.    How  many  are  green  ? 

19293949596979899 
91929394959697989 


PUPILSREADINGSIMPLE    WORDS,     47 


New  Class  Exercise. 

Purpose. — To  teac?t  to  recognize  instantly  the 
two  parts  which  make  each  of  the  numbers  from  2 
to  1O. 

Method. — Begin  with  5,  as  this  gives  more  variety  than  2,  3, 
or  4.  Show  that  4  +  1  or  1  +  4,  3  +  2  or  2  +  3,  make  5.  Drill  upon 
it  until  the  pupils  can  recognize  at  sight  the  two  component  parts 
of  5.  So  teach  the  component  parts  of  each  of  the  other  numbers 
from  2  to  10  ;  thus,  of  6  they  are  5  +  1  or  1  +  5,  4  +  2  or  2  +  4,  and 
3  +  3.  Of  7  they  are  6  +  1  or  1  +  6,  5  +  2  or  2  +  5,  4  +  3  or  3  +  4;  etc. 

Write  these  combinations  promiscuously  on  the  blackboard,  and 
require  the  pupils  to  give  the  sum  of  any  couplet  instantly  as  you 
point  to  the  couplet.  Remember  that  to  recognize  the  sum  at 
sight  is  quite  as  important  as  to  do  it  when  the  numbers  are  given 
orally,  and  that  the  pupil  may  do  one  readily  and  not  the  other. 

Having  a  large  number  of  figures  on  the  blackboard  or  on  a 
chart  before  the  class,  point  to  one  figure,  as  4,  and  then  to  an- 
other, as  3,  and  train  the  pupils  till  they  can  give  the  sum  "  as 
quick  as  thought." 

An  exercise  like  this  will  be  very  useful  both  for  its  own  sake 
and  as  a  preparation  for  subtraction :  Teacher,  "  I  will  give  one  of 
the  parts  of  8  and  the  class  may  give  the  other."  T.,  "  5  ;  "  C., 
"3;"  T.,  "4;"  C.,  "4;"  T.,  "  6 ;"  C.,  "  2,"  etc. 


Seat  Exercise. 

1.  Write  each  two  numbers  which  make  2. 

2.  Write  each  two  numbers  which  make  3. 

3.  Write  each  two  numbers  which  make  4.    Each  two 
which  make  5.    Each  two  which  make  6  ;  7  ;  8  ;  9  ;  10. 


ADDITION.— EXERCISES   FOR 


LESSON     III.  • 

Purpose. — To  teach  how  to  add  any  number  ex- 
pressed by  two  figures,  to  any  one  expressed  by  one 
figure. 

Method. — The  first  four  exercises  are  learned  by  a  simple 
recognition  of  the  meaning  of  the  words  thirteen,  fourteen,  etc. 


Class  Exercise. 

Write  10  in  one  place  on  the  board  and  7  in  another.  "  What 
is  this  ? "  (Ten.)  "  What  is  this  ?  "  (Seven.)  "  Ten  and  seven 
are  how  many  ?  "  "  What  do  we  call  ten  and  seven  ?  "  Question 
them  until  they  recall  the  fact  that  ten  and  seven  are  (or  are 
called)  seventeen.  Thus  proceed  with  10  and  8,  10  and  4,  10  and 
9,  etc.  This  is  a  review  of  the  process  of  counting  from  ten  to 
twenty,  but  is  now  to  be  seen  in  a  slightly  different  light. 

Write  10  +  1-  ,10  +  4=  ,10+6=  ,  etc.,  and  teach 
them  to  fill  the  blanks,  and  perform  the  following  seat  exercise. 


Seat  Exercise. 

10  +  1  = 

*10  +  4  = 

10  + 

=  19 

10  +  2  = 

10  +  9  = 

10  + 

=  15 

10  +  3  = 

10  +  1  = 

10  + 

=  16 

10  +  4  = 

10  +  3  = 

10  + 

=  17 

10  +  5  = 

10  +  5  = 

10  + 

=  18 

10  +  6  = 

10  +  2  = 

10  + 

=  12 

10  +  7  = 

10  +  8  = 

10  + 

=  13 

10  +  8  = 

10  +  6  = 

10  + 

=  14 

*  It  is  not  necessary  that  these  he  taken  in  the  reverse  order,  as  4  +  10,  9  +  10, 
etc.,  as  the  combinations  do  not  occur  in  this  order  in  ordinary  addition. 


PUPILS  READING   SIMPLE    WORDS.       49 

1.  There  were  ten  eggs  in  the  nest,  and  the  hen  laid 
three  more.     How  many  were  there  then  ? 

2.  John   has  ten 
books    and     Frank 
gives  him  five.   How 
many  books  has  he 
then? 

3.  Mary   has    10 
flowers.    How  many 
more  must  she  pick 
to  have  16  ? 

4.  There  are  10  birds  in  the  barn.     How  many  more 
must  come  to  make  18  ? 

5.  Ten  and  how  many  make  13  ? 

6.  Ten  and  how  many  make  17? 

5876410939 
10     10     10     10     10     10     10     10     10     10 


Recitation  and  Class  Exercises. 

The  recitations  and  class  exercises. in  this  lesson  will  be  similar 
to  those  in  the  last.  Many  other  exercises  like  those  in  the  Seat 
Exercises  will  be  given  orally.  In  general,  such  recitation  and 
class  exercise  will  consist,  First,  in  an  examination  of  slates,  to  see 
if  all  has  been  done  correctly  and  neatly ;  Second,  with  books  in 
hand,  the  pupils  will  read  the  seat  exercises  and  tell  the  answers, 
one  pupil  reading  the  problem  and  another  giving  the  answer ; 
Third,  other  exercises  will  be  dictated  by  the  teacher ;  Fourth,  con- 
cert exercises  on  the  Addition  Table,  and  exercises  in  adding  num- 
bers written  on  the  blackboard. 


50 


ADDITION.— EXE  RCI SE  S  FOR 


Seat  Exerci8e* 


20  +  3  = 

30  +  5  = 

40  +  2= 

50  +  8 

20  +  6  = 

30  +  7= 

40  +  0  = 

50  +  1 

20  +  5  = 

30  +  9  = 

40  +  9  = 

50  +  0 

20  +  8  = 

30  +  0  = 

40  +  7  = 

50  +  7 

20  +  1  = 

30  +  1  = 

40  +  1  = 

50  +  6 

20  +  4= 

30  +  3  = 

40  +  3  = 

50  +  3 

20  +  2  = 

30  +  6  = 

40  +  5  = 

50  +  4 

20  +  9  = 

30  +  2  = 

40  +  8  = 

50  +  2 

20  +  7  = 

30  +  8  = 

40  +  6  = 

50  +  6 

20  +  0  = 

30  +  4= 

40  +  4= 

50  +  5 

1.  James  has  found  20  eggs,  and  Frank  has  found  7 
more  than  James.     How  many  has  Frank  found  ? 


2.  There  are  thirty  blackbirds  in  a  tree,  and  on  the 
ground  seven  more  than  in  the  tree.      How  many  birds 
are  there  on  the  ground  ? 

3.  There  were  50  birds  on  the  ground  under  a  tree  and 
9  more  came.     How  many  birds  were  there  then  ? 

4.  Ann's  father  was  40  years  old,  and  Mary's  father  is 
6  years  older.     How  old  is  Mary's  father  ? 


PUPILS  READING   SIMPLE    WORDS.       51 


5.  In  Frank's  garden  are  40  flowers ;  but  in  George's 
garden  there  are  7  more  than  in  Frank's.     How  many 


flowers  are  there  in  George's  garden  ? 


3 

50 


7 
40 


8 
20 


6 
30 


4 

20 


2 
50 


1 

40 


3 

30 


2 

50 


0 

20 


Seat  Exercise. 


60  +  6  = 

70  +  5  = 

80  +  8  = 

90  +  2 

60  +  2  = 

70  +  2  = 

80  +  2  = 

90  +  0 

60  +  5  = 

70  +  1  = 

80  +  7  = 

90  +  1 

60  +  8  = 

70  +  7= 

80  +  1  = 

90  +  7 

60  +  9  = 

70  +  8= 

80  +  4= 

90  +  9 

60  +  1  = 

70  +  4= 

80  +  6  = 

90  +  3 

60  +  0  = 

70  +  3  = 

80  +  0  = 

90  +  5 

60  +  4= 

70  +  0  = 

80  +  9  = 

90  +  6 

60  +  3  = 

70  +  6  = 

80  +  3  = 

90  +  4 

60  +  7  = 

70  +  9  = 

80  +  5  = 

90  +  8 

1.  James  has  80  nuts  and  finds  6  more.     How  many 
has  he  then  ? 

2.  If  Mary  has  70  flowers  and  Ann  gives  her  6  more, 
how  many  has  she  in  all  ? 

3.  If  George  saw  90  birds  and  Frank  saw  8  more  than 
George  did,  how  many  did  Frank  see  ? 

4.  John  has  10  cents  and  his  father  gives  him  7  more. 
How  many  has  he  then  ? 

5.  James  has  70  cents  in  a  box  and  5  cents  in  his  hand. 
How  many  cents  has  he  in  all  ? 

54732143678 
80     90     70     50     80     70     10     20     40     60     60 


52 


A  DDITION.— EXERCISES   FOR 


Second  Class  Exercise. 

Purpose. — 2"o  teach  ?iow  to  add  any  number  rep- 
resented by  one  digit  to  another  represented  by  two 
digits,  without  counting. 

To  teach  how  to  find  out  how  many  37  and  8  more  make,  8 
write  the  numbers  as  in  the  margin.  First,  fix  the  attention  37 
upon  the  fact  that  37  is  3  tens  and  7.  Use  the  picture  or  45 
other  objects.  Second,  7  and  8  more  make  15,  which  is  1  ten  and 
5.  So  we  have  4  tens  and  5,  or  45.  Use  the  picture  or  other 
objects.  There  must  be  no  counting.  The  point  is  to  show  that  we 
have  only  to  consider  the  sum  of  TWO  digits,  in  any  case.  In  like 
manner  illustrate  the  process  with  a  variety  of  examples. 

This  exercise  need  be  continued  only  long  enough  to  teach  how 
the  addition  is  effected.  The  two  succeeding  exercises  exhibit  the 
expedients  by  which  facility  is  obtained. 


7 
54 


5 

28 

8 
47 


6 

18 

9 

28 


Seat  Exercise. 

5 

4 

7 

3 

13 

12 

36 

42 

7 

6 

5 

8 

63 

19 

77 

86 

4 
69 

9 

81 


8 
45 

4 
33 


2 
18 

7 
15 


P  UPILS   READING    SIMPLE     WORDS.     53 


Third  Class   Exercise. 

Purpose. — 2o  teach  to  recog?iize  the  sum  of  any 
digit  added  to  any  number  represented  by  two  digits, 
by  remembering  what  digits  when  added  give  O,  /,  2, 
3,  4,  5,  etc.,  in,  iinits  place. 

Method. — Knowing  that  9  +  1,  8  +  2,  6  +  4,  and  5  +  5,  each 
makes  10,  the  pupil  is  to  be  taught  to  recognize  the  sum  in  such 
cases  as  the  following : 

123  123 

JL9      IS     _17       tc' ;     29      28_     27_ 

Of  these  there  will  be  81.      The  pupils  may  be  required  to  write 
them  all. 

So,  again,  by  knowing  that  9  +  2,  8  +  3,  7  +  4,  and  6  +  5,  each 
makes  11  (or  1  in  units  place),  the  pupil  is  to  be  taught  to  recognize 
the  sum  in  such  cases  as  the  following : 


2 

3 

4 

2 

3 

4 

19 

18 

17 

etc.  ; 

29 

28 

27 

etc.  ; 

2 

3 

4 

2 

3* 

4 

39 

38 

37 

etc.  ; 

49 

48 

47 

etc.  ; 

Of  these  combinations  there  are  72  in  all.  The  pupils  may  be 
required  to  write  them  all  as  a  seat  exercise. 

Another  seat  exercise  may  be  obtained  by  requiring  all  the  sim- 
ilar combinations  which  give  2  in  the  units  place  of  the  sum,  as, 

3455789 
19_     18_     17_    JL6     Jt5     _14     |3 

3456789 
_29     _28     _27      26     J25      24      23 

etc.,  etc.,  etc. 

Of  these  there  are  63. 

Proceed  in  like  manner  to  teach  the  combinations  which  give 
3,  4,  5,  0,  7,  8,  and  9,  respectively,  in  the  units  place. 


54  ADDITION.— EXERCISES    FOR 


Fourth  Class  Exercise. 

Purpose,,  —  This  exercise  is  bttt  a   modified  form 
of  the  preceding,  and  has  the  same  end  in  view. 

• 

Method.  —  Write  on  the  blackboard  a  line  like  the  following  : 
3333333333 


Then  call  attention  to  the  fact  that  as  4  and  3  make  seven,  14  and 
3  make  seven-teen,  24  and  3  make  twenty-seven,  etc.  ;  that  is, 
that  we  have  only  to  think  what  4  and  3  make  in  any  case.  As  a 
first  exercise  take  only  cases  in  which  the  tens  are  not  changed, 
and  give  several  seat  exercises  of  this  character. 

Passing  to  the  case  in  which  the  tens  change,  show  the  reason 
clearly  as  in  the  second  exercise,  but  make  it  specially  clear  that 
the  tens  are  only  one  more  in  any  case,  and  that  the  important 
thing  still  is  to  recognize  the  sum  of  two  figures.  Finally,  give 
seat  and  class  exercises  like  the  following  till  the  idea  is  fixed. 

2222222222 
3       13       23       33       43       53       63       73       83       93 


5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

4 

14 

24 

34 

44 

54 

64 

74 

84 

94 

5 

5 

5 

5 

5 

5 

5 

5 

5 

5 

6 

16 

26 

36 

46 

56 

66 

76 

86 

96 

8 

8 

8 

8 

8 

8 

8 

8 

8 

8 

4 

14 

24 

34 

44 

54 

64 

74 

84 

94 

7 

7 

7 

7 

7 

7 

7 

7 

7 

7 

6 

16 

26 

36 

46 

56 

66 

76 

86 

96 

There  are  100  such  combinations  for  each  digit.  Give  thorough 
drill  upon  them,  and  conclude  this  lesson  with  miscellaneous 
exercises,  continuing  the  lessons  until  the  pupils  can  recognize  the 
sum  in  any  such  case  as  readily  as  they  can  the  sum  of  two  digits. 


PUPILS  READING   SIMPLE    WORDS.       55 


New  Class   Exercise. 

An  excellent  set  of  exercises  can  be  supplied  by  the  teacher 
thus  : 

Teach  them  to  count  one  hundred  by  twos,  as  2,  4,  6,  8,  10,  etc., 
to  100.  Then  again,  by  beginning  with  one,  count  on  by  twos,  as 
1,  3,  5,  7,  9, 11,  etc.,  to  99. 

When  this  is  learned,  teach  them  to  count  by  threes,  first  begin- 
ning with  3,  then  with  2,  and  then  with  1.  Thus  they  will  count 
"  3,  6,  9,  12,  15,  etc.,  to  99;"  or  "2,  5,  8,  11,  14,  etc..  to  98;"  or 
"1,4,  7,  10,13,  16,  etc.,  to  100." 

Again,  count  by  fours,  first  beginning  with  4,  then  with  3,  then 
with  2,  then  with  1. 

Again,  count  by  fives,  by  sixes,  etc. ,  to  nines,  in  each  case  start- 
ing with  each  lower  number. 

This  will  readily  be  seen  to  be  a  most  important  exercise,  and 
one  that  should  be  kept  up  for  days,  and  perhaps  for  weeks,  though 
it  need  not  prevent  the  pupils  from  going  on  in  the  book,  but  may 
be  made  a  frequent  oral  or  slate  exercise,  as  thought  best  by  the 
teacher. 

For  Seat  Exercises  of  this  kind,  tell  them  to  write  the  numbers 
up  to  100  by  twos,  as  2,  4,  6, 8, 10,  etc.,  and  so  of  all  the  other  com- 
binations here  suggested. 


Seat  Exercise. 

1.  How  is  Mary  counting  when  she  says  "  3,  9,  15,  21, 
etc."  ?     Count  thus  to  99. 

2.  How  is  one  counting  who  says  "2,  10,  18,  26,  etc."? 
Count  thus  to  98. 

3.  How  is  John  counting  when  he  says  "  7,  16,  25,  34, 
etc,"  ?     Count  thus  to  97. 

4.  By  what  is  James  counting  when  he  says  "5,  9,  13, 
17,  etc."  ?    Count  thus  to  97. 


56 


ADDITION.— EXERCI SES    FOR 


LESSON    IV, 

Purpose. — 2b  teach  how  to  add  any  number  of 
numbers  expressed  by  one  figure  each,  whose  entire 
sum  does  not  exceed  one  hundred. 


First  Exercise.* 


i 


1.  Here  is  an  old  barn,  and  in  the  yard  are  4  hens  with 
chickens.  One  hen  has  5  chickens,  another  has  8,  another 
has  6,  and  the  other  has  7.  How  many  chickens  are 
there  in  all ?  How  many  are  5  +  8  +  6  +  7? 


*  Hereafter,  suggestions  upon  class  exercises  and  recitations  will  be  put  in 
foot-notes.  Every  neiv process  should  be  introduced  by  «  familiar  class  exercise 
which  will  prepare  the  pupils  to  perform  the  seat  exercise  intelligently. 

The  class  exercise  to  be  given  before  this  seat  exercise  is  assigned,  will  con- 
sist in  showing  with  the  counters,  numeral  frame,  pictures  such  as  those  on 
pages  10,  11, 19,  or  other  objects,  how  to  add  several  numbers  expressed  by  one 
figure  each.  Thus,  suppose  we  wish  to  add  5,  4,  3,  7,  and  6.  Have  one  pupil 


PUPILS   READING  SIMPLE    IV  0  R  D  S.     57 


2.  Mary  has  4  flowers  and  Jane  gives  her  3  more.    How 
many  has  she  then  ?     She  then  finds  2  more.   How  many 
has  she  then?     AVhcn  she  brings  them  in,  her  mother 
gives  her  1  more.     How  many  has  she  in  all  ?   How  many 
are  4  +  3  +  2  +  1  ? 

3.  How  many  are  4  and  8  ?     How  many  are  12  and  5  ? 
How  many  are  17  and  6  ?     Then  how  many  are  4  +  8  + 

5  +  6? 

4.  Here  is  a  beautiful  plant. 
On  one  stem  are  5  flowers, 
on  another  7,  on  another  6, 
and   on   another    8.      How 
many  flowers   are   there   in 
all  ?     How  many  are  5  and 
7  ?     How  many  are  1 2  and 

6  ?     How  many  are  18  and 
8?      Thus,   how  many  are 
5+7+6+8? 

5.  Eight  apples  in  a  dish,  4  on  the  table,  7  on  the  floor, 
and  9  in  the  chair,  make  how  many  apples  ? 

6  +  4  +  8  +  5  +  3  =  how  many  ? 

7  +  6  +  4  +  3  +  2  +  1  +  5=  how  many? 


8 

9 

6 

5 

5 

6 

7 

2 

8 

4 

4 

4 

2 

3 

6 

7 

3 

3 

3 

3 

1 

4 

6 

2 

8 

2 

1 

4 

7 

4 

1 

7 

6 

4 

3 

1 

3 

2 

9 

put  5  counters  in  a  pile,  another  pupil  4  in  another  pile  near  the  first,  another 
pupil  3,  another  7,  and  another  6.  Then  let  them  see  clearly  what  the  purpose 
is,  viz. :  to  find  how  many  there  are  in  all  without  counting  them  one  by  one. 


58  ADDITION.— EXERCISES   FOR 

Second  Exercise. 

1.  Frank  bought  a  top  for  8  cents,  some  nuts  for  5 
cents,  a  kite  for  9  cents,  a  hoop  for  7  cents,  and  a  little 
book  for  6  cents.     How  many  cents  did  he  pay  for  all  ? 
84-5  +  9  +  7  +  61=  how  many  ? 

2.  Mary  bought  a  doll  for  54  cents,  a  little  book  for  8 
cents,  and  a  hoop  for  7  cents.     How  much  did  she  pay 
for  all  ?     54  +  8  +  7  =  how  many  ? 

3.  George  bought  a  sled  for  85  cents,  a  rope  for  8  cents, 
an  apple  for  1  cent,  and  some  nuts  for  3  cents.      How 
much  did  he  pay  for  all  ? 


4 

6 

9 

7 

6 

4 

3 

3 

7 

4 

8 

4 

5 

8 

4 

4 

6 

3 

4 

3 

8 

8 

5 

4 

4 

1 

3 

5 

7 

5 

5 

4 

3 

2 

2 

6 

6 

6 

8 

2 

5 

4 

5 

8 

7 

7 

7 

2 

2 

7 

1 

2 

4 

6 

7 

9 

8 

6 

4 

1 

9 

7 

2 

8 

3_|_4  +  5  +  8+7  +  5+4+9  =  how  many? 
54-8  +  2  +  1  +  1  +  3  +  3  +  4  =  how  many? 


Put  the  4  with  the  5  and  ask,  "  How  many  in  this  pile  ?"  (9.)  Then  the  3, 
asking  as  before  ;  then  the  7,  then  the  6.  Show  also  how  to  add  the  numbers 
when  written  in  a  column,  and  when  written  5  +  4  +  3  +  7  +  6. 

When  the  pupil  hesitates  in  adding,  as  when  he  has  29  and  the  next  figure  is 
7,  ask,  "  9  and  7  give  what  figures  ?  "  thus  teaching  him  to  use  the  knowledge 
already  gained.  Pupils  must  be  trained  in  this  manner  so  that  they  will  not 
think  of  counting. 

These  exercises  are  by  no  means  sufficient  to  secure  facility  in  adding. 
Weeks  of  drill  are  necessary.  This  may  be  kept  up  as  a  daily  exercise  while  the 
pupil  proceeds  with  other  lessons. 


PUPILS   READING   SIMPLE    WORDS.      59 


LESSON    V. 

Definition  Exercises. 

.—  ^  teach  the  Meaning  of  the  words 
Number,  Add,  Addition,  Sum,  and  Amount,  so  that 
the  ptipil  can  understand  them  w?ien  used,  and  can 
ttse  them. 

Method. — Ask  questions  involving  the  word,  and  if  the  child 
does  not  catch  the  meaning,  put  the  question  in  a  familiar  form, 
and  repeat  the  process  till  the  purpose  is  accomplished.* 

First  Exercise. \ 


1.  What  number  of  boys  do  you  see  in  the  picture  ? 
What  number  of  men  ?  What  Dumber  of  trees  ? 

*  Formal  definitions  are  out  of  place  here,  and  all  such  questions  as  "  What 
is  number?"  u  What  is  Addition  ?"  etc.  To  teach  to  perceive  and  to  conceive 
constitute  the  purpose  now  ;  to  formulate  thought  is  a  later  process,  and  to  ob- 
tain ideas  from  formal  statements  and  definitions  a  still  later  one. 

t  This  must  be  preceded  by  an  oral  class  exercise.  1.  Print  the  word 
N  u  m  b  e  r  on  the  board,  and  teach  it,  if  necessary.  Then  ask,  "  Wh&tnumber 

' 


"         .  •    -. 


60  ADDITION.— EXERCISE  S   FOR 

2.  How  many  ducks  do  you  see  in  the  picture  ?    Ask 
the  same  question  and  use  the  word  number.    Ask  the 
same  question  about  the  barrels  and  use  the  word  num- 
ber. 

3.  If  you  add  the  number  of  men  in  the  picture  to  the 
number  of  boys,  what  number  does  it  make  ?    If  you  add 
the  number  of  barrels  to  the  number  of  ducks,  what  is 
the  sum  ? 

4.  If  you  add  the  number  of  trees,  barrels,  and  ducks, 
what  is  the  sum?     What  other  word  can  you  use  for 
sum? 

5.  Ask  a  question  like  the  last  about  the  trees,  men, 
and  boys. 

6.  What  will  be  the  sum  if  you  add  the  number  of  boys 
and  the  number  of  ducks  ?     Ask  the  same  question  about 
the  trees  and  ducks.     About  the  boys  and  trees. 

7.  If  you  add  the  number  of  your  eyes,  the  number  of 
your  hands,  and  the  number  of  your  feet,  what  is  the 
sum? 

of  hands  have  you,  John  ?  "  "  What  number  of  fingers  have  you,  Mary  ?  "  etc. 
If  they  do  not  answer  readily,  put  the  question  thus  :  "  How  many  hands  have 
you  ?  "  Then  put  it  as  before.  Then  of  objects  out  of  sight.  "  What  number 
of  legs  has  a  kitten?"  etc.  Again,  put  figures,  as  5,  3,  10,  32,  87,  etc.,  on  the 
board,  and  ask,  "  What  number  is  this  ?  "  "  What  number  is  this  ?  "  etc.  Num- 
ber means  how  many,  is  the  child  form  of  the  thought. 

2.  "  If  I  add  the  numbers  5  and  3,  what  number  does  it  make  ?  "    So  of  other 
numbers.    If  they  do  not  catch  the  meaning,  ask  "  If  I  put  together  the  numbers 
5  and  3,  how  many  does  it  make  ?  "  or,  "  What  number  does  it  make  ?  " 

3.  "  If  I  add  3  and  4.  what  is  the  sum?"  or,  "  If  I  add  3  and  4,  how  many 
does  it  make  ?  "  etc.   "  If  I  add  the  numbers  1  and  8,  what  number  is  the  sum?" 
etc.    TJse  the  word  amount  in  the  same  manner.    Sum  or  amount  means  how 
many  it  makes,  will  be  the  child  thought. 

4.  "  In  all  your  lessons  for  some  time  you  have  been  putting  numbers  to- 
gether to  find  out  how  many  they  make.    (Turn  back  and  show  them  this.) 
This  is  called  Addition.    What  have  you  been  studying?    What  is  putting 
numbers  together  to  find  how  many  they  make  called  ?  " 


PUPILS   READING   SIMPLE    WORDS.       61 


Second  Exercise. 

1.  What  is  the  sum  of  5,  8,  4,  7,  and  6  ? 

2.  What  is  the  sum  of  27  and  8  ? 

3.  What  is  the  amount  of  15,  4,  and  7  ? 

4.  What  is  the  amount  of  7,  9,  8,  and  4  ? 

5.  What  is  the  sum  of  63  and  5  ? 

6.  What  is  the  amount  of  81  and  9  ? 

7.  What    do   yon    call   finding   the   sum   of  several 
numbers? 

8.  Add  the  numbers  8,  4,  7,  6,  5. 

9.  Add  the  numbers  10,  4,  8,  7,  9. 

10.  What  number  added  to  5  makes  9  ? 

11.  What  number  added  to  3  makes  7  ? 

12.  What  number  added  to  7  makes  15  ? 

13.  What  number  added  to  9  makes  13  ? 

14.  Find  the  sum  of  8,  7,  6,  4,  and  3. 

15.  Find  the  amount  of  20,  6,  8,  4,  and  2. 

16.  When  you  put  several  numbers  together,  what  do 
you  call  the  number  which  they  make  ? 


SUBTRACTION.— EX ERCI SES  FOR 


SUBTRACTION. 

Purpose. — To  teach  how  to  recognize  the  re- 
mainder when  any  number  less  than  70  is  taken 
from  any  number  which  is  composed  of  that  num- 
ber and  any  number  less  than  ?0. 

Method. — Consider  what  it  takes  with  the  given  number  to 
make  the  one  from  which  it  is  to  be  taken. 

Illustrate  with  Counters,  and  with  the  Numeral  Frame,  that  as 
5  and  4  make  9,  4  from  9  leaves  5,  and  also  that  5  from  9  leaves  4. 
Be  sure  that  both  facts  are  recognized. 

First  Exercise, 

1.  There  are  3  pinks  on  a  stock. 
How  many  will  be  left  if  you  pick 
one  ?  The  one  picked  and  the  2  left 
are  how  many  ?     1  and  what  make 
3  ?     1  from  3  leaves  how  many  ?    3 
less  1  is  how  many  ? 

2.  If  you  were  to  pick  two  of  the 
pinks,  how  many  would  be  left  ?  The 

2  picked   and  the  1   left  are  how 

many  ?  2  and  what  make  3  ?  2  from  3  leaves  how  many  ? 

3  less  2  is  how  many  ? 

3.  If  you  have  7  apples  in 
two  piles,  and  there  are  3  in 
one  pile,  how  many  are  there 
in  the  other  ?     3  and  what 
make  7  ?     3  from  7  leaves 
how  many  ? 


PUPILS  READING   SIMPLE    WORDS.      63 

4.  If  you  take  4  apples  from  a  pile  of  7  apples,  how 
many  will  be  left  ?     Why  ?      (Because  4  and  3  make  7.) 
7  less  4  is  how  many  ?     7  less  3  is  how  many  ? 

5.  Two  and  5  make  how  many  ?     2  from  7  leaves  how 
many  ?     Why  ?     5  from  7  leaves  how  many  ?     Why  ? 

6.  A  boy  has  G  cents  in  one  pocket  and  3  cents  in  the 
other.     How  many  has  he  in  all  ?      What  do  G  and  3 
make  ?    If  the  boy  loses  the  3  cents  out  of  one  pocket, 
how  many  has  he  left  ?  How  many  had  he  at  first  ?  How 
many  did  he  lose?     How  many  has  he  left  ?     3  from  9 
leaves  how  many  ?    Why  ? 


1+ 

=  1 

1  from    1  leaves  how  many? 

1  —  1=  * 

1+ 

o 

1  from    2  leaves  how  many? 

2  —  1  = 

1+ 

=  3 

1  from    3  leaves  how  many  ? 

3-1  = 

1+ 

=  4 

1  from    4  leaves  how  many  ? 

V 

4—1  = 

1+ 

=  5 

1  from    5  leaves  how  many  ? 

5-1  = 

1+ 

=  6 

1  from    6  leaves  how  many  ? 

6  —  1  = 

1+ 

=  7 

1  from    7  leaves  how  many  ? 

7-1  = 

1+ 

0 

1  from    8  leaves  how  many  ? 

8-1  = 

1+ 

=  9 

1  from    9  leaves  how  many  ? 

9  —  1  = 

1+ 

=  10 

1  from  10  leaves  how  many? 

10  —  1  = 

1 

23456789     10       12 

1 

111111111.00 

7.  Count  backward  from  1.0  to  0,  by  1  ;    thus,  10,  9, 
8,  etc.     From  9  to  0.     From  8  to  0. 

8.  Count  backward  from  7  to  0,  by  1 ;  thus,  7,  G,  5,  etc. 
From  6  to  0.     From  5  to  0.     From  4  to  0.     From  3  to  0. 

This  is  an  important  Drill  Exercise,  and  the  teacher  should  be 
careful  to  have  it  thoroughly  understood. 

*  Teach  how  to  read  this  column.    This  and  the  corresponding  columns  in 
the  subsequent  exercises  are  to  be  thoroughly  memorized. 


64 


SUBTRACTION.— EXE  RCI SE  S   FOR 


Second  Exercise. 

1.  There  are  6  ducks 
in  the  pond.     If  2  of 
them  should  come  out, 
how    many    would  re- 
main ?    2  and  what  are 

6  ?  2  from  6  leaves  how 
many  ?    6  less  2  is  how 
many? 

2.  There   are  5  eggs 

in  the  upper  nest  and  2  in 
the  lower.  How  many  more 
eggs  are  there  in  the  upper 
than  in  the  lower  ?  2  and 
how  many  more  make  5  ? 
2  from  5  leaves  how  many  ? 

3.  Mary  has  7  cents  and 
Frank  has  2.      How  many 
more  has  Mary  than  Frank? 
2  and  how  many  more  make 

7  ?     2  from  7  leaves  how 
many? 

4.  Henry  is  2  years  old.    How  many  more  years  must 
he  live  to  be  5  years  old?    2  and  how  many  make  5  ?    2 
from  5  leaves  how  many  ? 

5.  Make  7  marks  in  a  row  on  your 
slate.     Then  make  two  marks  under 
them.     How  many  marks  have  you  in 
all  ?    If  you  take  away  the  2  marks, 


PUPILS   READING    SIMPLE     WORDS.     65 


how  many  of  the  9  marks  will  remain  ?     2  from  9  leaves 

how  many?  2  and  how  many  make  9?  9—  2  is  how  many? 

2+      =  2 

2  from    2  leaves  how  manv  ? 

V 

2—2  = 

2+      =  3 

2  from    3  leaves  how  many  ? 

3-2  = 

2-f-      =  4 

2  from    4  leaves  how  many  ? 

4  —  2  = 

2+      =  5 

2  from    5  leaves  how  many  ? 

5—2  = 

2+      =   6 

2  from    6  leaves  how  many? 

6  —  2  = 

2+     =  7 

2  from    7  leaves  how  many  ? 

7  —  2  = 

2+     =  8 

2  from    8  leaves  how  many  ? 

8-2  = 

2+      =  9 

2  from    9  leaves  how  many  ? 

9-2  = 

2+     =10 

2  from  10  leaves  how  many  ? 

10  —  2  = 

2+      =11 

2  from  11  leaves  how  many  ? 

11—2  = 

23456789     10     11       23 

222222222200 

Drill  Exercise. — Conclude  each  of  these  lessons  by  drill  exercises 
in  counting  backward  ;  thus,  here  have  the  pupils  count  backward 
from  11  to  0,  by  2  ;  then  from  10  ;  then  from  9,  etc.  Conclude  the 
next  exercise  by  counting  backward  from  12  to  0,  by  3,  etc. 


Third  Exercise. 

1.  Little  May  is  but  3  years 
old,  and  her  brother  Frank  is  7 
years  old.    How  many  years  older 
is  Frank  than  May  ?    3  and  how 
many  make  7  ?     3  from  7  leaves 
how  many  ? 

2.  Make  9  dots  on  your  slate, 
putting  3  in  one  group  and  6  in 
another.     3  and  how  many  make 
9  ?     3  from  9  leaves  how  many  ? 


66 


SUBTRACTION.— EXE RCI SES   FOR 


'  '  \r\.     i   Al*Mi\ll>  I     '  J 

i    ^'"l  'ifip  ^l-,'    ~? 

'I!  I"*!  i.."  ' IK'S  in'  III' 


3.  A  man  had  lost  3  fingers  from   one  hand.    How 
many  had  he  left  on  that 

hand,  counting  the  thumb  ? 

4.  There  are  8  books  on 
the  table.    How  many  will 
be   left   when   Frank   has 
taken    the    3    small   ones 
away  ?    3  and  what  make 
8  ?    3  from  8  leaves  how 


many 

V 

3  + 

=  3 

3  + 

=   4 

3  + 

=  5 

3  + 

=   6 

3  + 

tv 

3  + 

=  8 

3  + 

=  9 

3  + 

=  10 

3  + 

=  11 

3  + 

=  12 

3 

4      5 

3 

3       3 

3  from    3  leaves  how  many  ? 

3  from    4  leaves  how  many  ? 

3  from    5  leaves  how  many  ? 

3  from    6  leaves  how  many  ? 

3  from    7  leaves  how  many  ? 

3  from    8  leaves  how  many  ? 

3  from    9  leaves  how  many  ? 

3  from  10  leaves  how  many  ? 

3  from  11  leaves  how  many  ? 

3  from  12  leaves  how  many  ? 
6       7       8       9       10       11 
3333         3         3 


3-3  = 

4—3  = 

5—3  = 

6—3  = 

7-3  = 

8-3  = 

9-3  = 

10  —  3  = 

11-3  = 

12-3  = 

12      3       5 

300 


Fourth  Exercise. 


1.  John  is  now  10 
years  old,  but  he  be- 
gan going  to  school  4 
years  ago.  How  old 
was  he  when  he  began 
to  go  to  school  ?  4  and 
what  make  10?  4  from 
10  leaves  how  many  ? 


^jess  «!•; 

^  y  *~j 

<S~J,r^H\«jfe^fe^^^Tj^  .1  *'• 


/t&e^imem 

•  6f?    jSJS&Sr*. 

<>•   ,.N«-  A 


PUPILSREADING    SIMPLE    WORDS.    C7 


&-&*&&wmm. 


/      .-  V:v^'\VV  ViFrTi   \K  •  i-V*- 

,/  Iki^iiwM 


, 


2.  Little  May  is  but  4  years  old.      How  many  years 
before  she  will  be  11  years  old  ?    4  and  what  make  11  ? 
4  from  11  leaves  how  many  ? 

3.  Five  tops  and  4  tops  are  how  many  tops  ? 

4.  Nine  tops  are  how  many  more  than  5  tops  ? 

5.  Nine  tops  are  how  many  more  than  4  tops  ? 

6.  Mary  has  13  cents  and  Carrie  has  4.     How  many 
more  has  Mary  than  Carrie  ? 


4  + 

=  7 

4  + 

=  10 

4  + 

=  4 

4  + 

=  13 

4  + 

=  9 

4  + 

=  11 

4  + 

=  5 

4  + 

=  8 

4  + 

=  6 

4  + 

=  12 

11 

6       5 

4 

4      4 

4  from  4  leaves  how  many  ? 
4  from  5  leaves  how  many  ? 
4  from  6  leaves  how  many  ? 
4  from  7  leaves  how  many  ? 
4  from  8  leaves  how  many  ? 
4  from  9  leaves  how  many  ? 
4  from  10  leaves  how  many  ? 
4  from  11  leaves  how  many  ? 
4  from  1 2  leaves  how  many  ? 

«/ 

4  from  13  leaves  how  many  ? 

4"     12       10       13       8       7 
444444 


10—4= 
8—4= 
4—4= 
6  —  4= 

11—4= 
9  —  4  = 
5—4  = 
7-4= 

13—4= 

12  —  4= 

945 
400 


68         SUBTRACTION.— EXERCISES  FOR 


Fifth  Exercise. 

1.  How  many  birds  are  in 
the   tree  ?     How   many  are 
flying  to   the   tree?      How 
many  more  are  there  in  the 
tree  than  flying  to  it?     If 
as  many  should  fly  off  from 
the  tree  as  are  flying  to  it, 
how  many  would  be  left  in 
the  tree  ?      8  less  5  is  how 
many  ?  8  is  how  many  more 
than  5  ? 

2.  If  you  have  5  apples,  how  many  more 
to  have  12  ?     12  is  how  many  more  than  5 
leaves  how  many  ? 

3.  How  many  days  in  one  week  ?    After 
week  are  gone,  how  many  are  left  ?   7  —  5  = 


must  you  get 
?    5  from  12 

5  days  of  a 
how  many  ? 


5+     =  8 

5  from    5  leaves  how  many  ? 

11  —  5  = 

5+     =  6 

5  from    6  leaves  how  many  ? 

6  —  5  = 

5+      =11 

5  from    7  leaves  how  many  ? 

8  —  5  = 

5+      =  9 

5  from    8  leaves  how  many  ? 

10—5  = 

5+      =  5 

5  from    9  leaves  how  many  ? 

13—5  = 

5+      =  7 

5  from  10  leaves  how  many  ? 

12—5  = 

5+      =12 

5  from  11  leaves  how  many  ? 

7-5  = 

5+     =14 

5  from  12  leaves  how  many  ? 

5-5  = 

5+      =10 

5  from  13  leaves  how  many  ? 

9  —  5  = 

5+     =13 

5  from  14  leaves  how  many  ? 

14-5  = 

12       8       7      10      5       9       6       11       13      14      5      6 

555555555500 

PUPILS  READING  SIMPLE    WORDS.       69 


Sixth  Exercise. 

1.  If  I  buy  a  book  for  6  cents,  and  hand 
the  bookseller  a  dime  (ten  cents),  how 
much  change  must  he  give  me?     6  and 
what  are  10  ?   6  from  10  leaves  how  many  ? 

2.  If  I  owe  the  postmaster  6  cents,  and  hand  him  15 
cents,  how  much  change  must  he  give  me  ?     6  and  what 
make  15  ?     6  from  15  leaves 

how  many  9 

3.  There  were  15  peaches 
on  the  tree.     How  many  are 
there  now  ?   Jane  picked  the 
others.     How  many  did  she 
pick  ? 

4.  There  were  15  peaches 
on  the  tree,  and  Jane  picked 


6  of  them.  How  many  are  left  ?      Jffe  >• 


64- 

—  10 

6  from    6  leaves  how  many  ? 

6-6  = 

6  + 

w 

6  from    7  leaves  how  many  ? 

10  —  6  = 

6  + 

=  9 

6  from    8  leaves  how  many  ? 

15  —  6  = 

6  + 

=  11 

6  from    9  leaves  how  many  ? 

13-6  = 

64- 

=   6 

6  from  10  leaves  how  many  ? 

12-6  = 

6-h 

=  12 

6  from  11  leaves  how  many? 

8-6  = 

6  + 

=  14 

6  from  12  leaves  how  many  ? 

9-6  = 

6  + 

=  8 

6  from  13  leaves  how  many? 

7-6  = 

6  + 

=  13 

6  from  14  leaves  how  many? 

11  —  6  = 

64- 

=  15 

6  from  15  leaves  how  many? 

14  —  6  = 

12 

6       8       7       11       13       15       14      9      10      6      3 

6 

666         6         6         6         66600 

t 

T 

70 


SUBTRACTION.— EXERCISE  S  FOR 


Seventh  Exercise. 

1.  John  had  11  cents,  and  bought  a  slate  for  7  cents. 
How  many  cents  did  he  have  left  ?     7  and  what  make 
11  ?     7  from  11  leaves  how  many  ? 

2.  Frank  has  7  cents.     How  many  more  must  he  earn 
to  have  13  cents  ? 

3.  Mary  has   15  flowers  and  her  brother  Henry  has  7. 
How  many  more  has  Mary  than  Henry  ? 

4.  From  a  flock  of  12  chickens  a  fox  caught  7.    How 
many  were  left  ? 

5.  Frank  had  a  ball  worth  16  cents,  and  James  had  a 
top  worth  7  cents.     How  much  more  is  the  ball  worth 
than  the  top  ?     If  they  trade,  how  many  cents  ought 
James  to  give  to  Frank  besides  giving  him  his  top  ? 

6.  If  a  spool  of  thread  is  worth  7  cents,  and  I  hand  the 
merchant  10  cents  for  one,  how  much  change  must  he 
give  me  ? 

7  from    7  leaves  how  many  ?  7 — 7= 

7  from    8  leaves  how  many?  10—7  = 

7  from    9  leaves  how  many?  16  —  7= 

7  from  10  leaves  how  many?  8  —  7  = 

7  from  11  leaves  how  many?  11  —  7  = 

7  from  12  leaves  how  many?  15  —  7= 

7  from  13  leaves  how  many?  12 --7  = 

7  from  14  leaves  how  many?  9—8  = 

7  from  15  leaves  how  many?  13  —  7  = 

7  from  16  leaves  how  many?  14—7= 


7  + 

=  9 

7  + 

=  15 

7  + 

=  10 

7-f 

Q 

7  + 

=  11 

7  + 

=  13 

7  + 

=  12 

7  + 

=  14 

7  + 

=  7 

7  + 

=  16 

16      12      7      8 

7777 


10      11      13      14      9      15      7    4 

7        7        7        77        700 


P  UPILS  READING   SIMPLE    WORDS.       71 


Eighth  Exercise. 


1.  Mary  had  13  cents,  and  bought  a  ribbon  for  8  cents. 
How  many  cents  had  she  left  ?     8  and  what  make  13  ? 

2.  John  bought  a  lead-pencil  for  8  cents,  and  handed 
the  merchant  15  cents.     How  much  change  must  he  re- 
ceive ?     8  and  what  make  15  ?    8  from  15  leaves  how 
many  ? 

3.  When  May  had  learned  17  words,  her  brother  Frank 
had  learned  8  less.     How  many  had  Frank  learned  ? 

4.  6  and  8  are  how  many  ?     6  from  14  leaves  how 
many  ?    8  from  14  leaves  how  many  ?    How  would  you 
illustrate  this  with  the  counters  ? 


8  + 

=  12 

8  from    8  leaves 

8  + 

=  10 

8  from    9  leaves 

8  + 

0 

8  from  10  leaves 

8  + 

=  9 

8  from  11  leaves 

8  + 

=  17 

8  from  12  leaves 

8  + 

=13 

8  from  13  leaves 

8  + 

=  15 

8  from  14  leaves 

8  + 

=  14 

8  from  15  leaves 

8-f 

=11 

8  from  16  leaves 

8  + 

=  16 

8  from  17  leaves 

how  many  ? 
how  many  ? 
how  many  ? 
how  many? 
how  many? 
how  many? 
how  many? 
how  many? 
how  many? 
how  many? 


11-8: 

15  —  8: 

17-8: 
8—8- 

10  —  8: 
12-8: 
14  —  8: 
9-8: 
13-8: 

16  —  8: 


8      10      9      17     15     11     13     12     16     14     83 

8        88        888888800 


SUBTRACTION.— EXERCISES  FOR 


Ninth  Exercise. 

1.  Make  17  marks  on  your  slate  in  two  rows,  9  in  one 
row,  and  8  in  another  row  right  under  the  first  row.   How 
many  marks  have  you  now  in  all  ?    If  you  take  the  9 
away  from  the  17,  how  many  will  remain  ?     If  you  take 
away  the  8  from  the  17,  instead  of  the  9,  how  many  will 
remain  ?     9  from  17  leaves  how  many  ?     Why  ? 

2.  If  you  take  9  from  16,  how  many  will  remain  ? 
Why  ?    How  would  you  illustrate  it  with  the  counters  ? 

3.  James  bought  a  book  for  9  cents,  which  took  all  the 
money  he  had  but  4  cents.     How  much  did  he  have  at 
first  ?     9  from  13  leave  how  many  ? 

4.  If  John  buys  a  ball  for  9  cents,  and  hands  the  mer- 
chant 1 5  cents,  how  much  change  should  he  receive  ? 

5.  Mary  is  18  years  old,  and  her  little  sister  Ann  is  but 
9.     How  much  older  is  Mary  than  Ann  ? 

9  leaves  how 

10  leaves  how 

11  leaves  how 

12  leaves  how 

13  leaves  how 

14  leaves  how 

15  leaves  how 

16  leaves  how 

17  leaves  how 

18  leaves  how 


9  + 

=  10 

9  from 

9-f 

=  17 

9  from 

9-f 

=  11 

9  from 

9  + 

=  15 

9  from 

9  + 

=  12 

9  from 

9  + 

=  9 

9  from 

9  + 

=  13 

9  from 

9  + 

=  18 

9  from 

9  + 

=  16 

9  from 

9  + 

=  14 

9  from 

many  ? 

12—9 

many? 

9-9 

many? 

11  —  9 

many  ? 

18-9 

many? 

16  —  9 

many  ? 

10—9 

many? 

13-9 

many? 

15  —  9 

many  ? 

14—9 

many? 

17  —  9 

17      9      10     15     18     12     14     16     11     13      9      5 
99        9999999900 


PUPILS  READING   SIMPLE    WORDS.       73 


-X- 


Definition  Exercise. 

1.  There  were  8  roses  on 
the  bush,  and  Mary  has  sub- 
tracted  3    of   them.      How 
many  are  there  left  ?    3  sub- 
tracted from  8  leaves  how 
many  ? 

2.  There  are  7  eggs  in  the 
nest.    If  you  subtract  3,  how 

V 

many  will  remain  ?     If  you 
subtract  4,  how  many  will 
remain  ?     If  you  subtract  3  from  7, 
what  is  the  remainder  ?    If  you  sub- 
tract 4  from  7,  what  is  the  remain- 
der ? 

3.  If  you  subtract  2  from  5,  what 
is  the  remainder  ?    If  you  subtract  3 
from  5,  what  is  the  remainder? 

4.  If  you  subtract  5  from  9,  what  is  the  remainder?   If 
you  take  5  from  9,  what  number  is  left  ?     (These  ques- 
tions mean  the  same  thing.) 

5.  If  you  subtract  2  from  8,  what  is  the  remainder  ?   If 
you  take  2  from  8,  what  number  is  left  ? 

6.  If  you  subtract  3  from  9,  what  is  the  remainder  ? 
Ask  this  question  without  using  the  words  subtract  and 
remainder. 

7.  If  you  take  8  from  12,  what  number  is  left  ?  Ask  the 
same  question  and  use  the  words  subtract  and  remainder. 

*  For  the  general  character  and  spirit  of  the  oral  exercise  which  precedes 
this,  see  foot-notes?,  pages  59,  60.  Subtract  and  remainder  are  the  words  whose 
use  is  to  he  taught  in  this  exercise. 


SUBTRACTION.— EXERCISES  FOR 


8.  Supply  the  proper  words  in  the  following : 

If  I 6  from  13,  what  is  the ? 

What  is  the when  you 7  from  11  ? 

When  you  —      —  8  from  17,  what  is  the ? 

What  is  the when  9  is from  20  ? 


Second  Definition  Exercise. 

1.  How  many  books  are 
on  the  table  ?     How  many 
are  on    the    chair?      How 
many  more  books  are  there 
on  the   table   than   on   the 
chair  ?     What  is  the  differ- 
ence between  8  books  and  5 
books  ? 

2.  If   an   orange  costs  7  cents  and  a  lemon  5  cents, 
what  is  the  difference  between  the  price  of  an  orange  and 
the  price  of  a  lemon  ?  What  is  the  difference  between  7  and  5? 

3.  What  is  the  difference  between  10  dollars  and  6 
dollars  ? 

4.  John  worked  9  hours  and  Henry  worked  5  hours. 
How  many  more  hours   did  John  work  than  Henry  ? 
What  is  the  difference  between  9  hours  and  5  hours  ? 

5.  What  is  the between  11  and  6  ? 

What  is  the  —         -  when  you  take  6  from  11  ? 
What  is  the  -        —  between  8  and  3  ? 

If  you 7  from  15,  what  is  the ? 


How  do  you  find  the 


—  between  10  and  7  ? 
Am.  I 7  from  10. 


PUPILS  READING   SIMPLE    WORDS.       75 

6.  What  number  does  4  -f-  7  make  ?     What  number 
does  3  +  2  make  ?  What  is  the  difference  between  11  and  5  ? 

7.  From  the  sum  of  4  and  3  subtract  5. 

8.  From  the of  2,  5,  and  6,  subtract  8  ? 

9.  Add  3,  4,  and  7,  and  from  the  amount  subtract  9. 
What  word  could  you  use  instead  of  amount  in  asking 
this  question  ?    What  instead  of  subtract  ? 

10.  From  3  +  2  +  4  +  1  subtract  7.     What  number  is 
3  +  2  +  4  +  1 ? 

11.  What  is  the  -       —  between  the of  5,  2,  and 

1,  and  3,  2,  and  2  ?   How  much  is  5  +  2  + 1  ?    How  much 

3  +  2  +  2? 


Drill  Exercises.* 

1.  4+3— 2  +  6  +  1— 8  +  5— 2=how  many? 

2.  5_ 2  +  7  —  6—3  +  8— 4  +  6=how  many  ? 

3.  1  +  2  +  3  +  4  +  5  — 9—2  +  7  — 6=how  many? 

4.  4_l_8  +  6  —  9— 4—1  +  7  —  8  +  6=how  many  ? 

5.  13_6— 4  +  7  —  5  —  8  —  3  +  7=how  many? 

6.  i7_9_5  +  2  +  8  —  6  +  4— l=how  many  ? 

7.  7  +  8  —  9— 2  +  6  —  7  +  2— 3=how  many  ? 

*  The  teacher  will  need  to  explain  fully,  and  illustrate  by  a  number  of 
examples,  before  the  pupils  are  required  to  study  these  exercises.  It  is  a 
most  valuable  exercise  for  class  drill.  Name  numbers  in  this  way,  and  let  the 
pupils  answer.  Thus,  at  first,  the  teacher  says,  "4  +  2"— the  pupils,  in  con- 
cert, "  6 ;"  the  teacher,  "  plus  5  "—the  pupils,  "  11 ;"  the  teacher,  "  minus  4"— 
the  pupils,  "  7,"  etc.  After  a  little  concert  answering  of  this  kind,  i.  e.,  after 
each  number,  let  all  follow  silently,  as  the  teacher  says,  "2  +  3  +  4—6-1+8= 
how  many  ?  "  Then  all  who  know  raise  the  hand.  If  their  results  do  not 
agree,  try  it  again  and  again.  Such  an  exercise  as  this  should  be  kept  up  for  a 
week  or  two  as  the  main  exercise  with  the  class,  and  should  always  be  used 
with  frequency  as  a  general  exercise  for  the  school.  For  the  more  advanced, 
it  may  include  multiplication  and  division. 


76          SUBTRACTION.—  EXERCISES   FOR 

8.  2  +  3  +  7  —  9  +  5  —  6  +  7  —  8=how  many  ? 

9.  6+7  +  5—  9  +  3—  8—2  +  7=how  many? 

10.  15—  8—  4—  2  +  6—  4—  2—  l=howmany  ? 

11.  16  —  7  —  6  +  4  +  2  —  6—  3  +  9=howmany? 

12.  11+2  —  6—  3  +  5  +  2—  4  +  1—  how  many? 

13.  10—  3—  2  +  7  —  8—3  +  6—  4=how  many? 

14.  6  +  9  +  2—  8—2  +  4—  6  +  3=how  many? 

15.  14—  6—  5  +  3  +  2—  3  +  2  +  4=how  many? 

16.  9  +  7_8—  2  +  3—  4—  3  +  7=how  many? 

17.  8  +  6  +  2  —  7—5  +  3  —  l  +  3=how  many? 
- 


18 
19 
20, 


+  6  +  2  —  7—5  +  3  —  l  +  3=how  many 
6  +  7  +  4—  9—3  +  6—  4  +  8=how  many? 
I.  3  +  8  +  2  —  7  —  6  +  4  +  5  —  9=how  many? 
>.  6—  4  +  2  +  2  +  3  +  3  —  6—  6=how  many? 


Practical   Exercises.* 

1.  John  had  5  cents  and  6  cents.     He  then  spent  8 
cents,  and  afterward  earned  4  cents.    How  many  had  he 
then  ? 

2.  Mary  was  very  fond  of  flowers.     She  had  8  little 
plants,  but  3  of  them  died.     Then  her  cousin  gave  her  4 
plants.     How  many  had  she  at  last 

3.  Henry  had  15  cents,  and  spent  6  cents  for  an  orange, 
1  cent  for  a  pencil,  and  3  cents  for  some  nuts.    How 
many  cents  had  he  left  ? 


*  The  teacher  should  illustrate  these  examples  by  using  the  counters  for 
cents.  Thus,  for  the  first,  put  out  five  counters  and  then  6.  Take  away  8 ; 
then  add  4.  Question  the  pupils  as  to  what  the  number  is  each  time. 


PUPILS  READING   SIMPLE    WORDS.       77 

4.  Frank  earned  6  cents  Monday,  spent  4  cents  Tues- 
day, earned  7  cents  Wednesday,  4  cents  Thursday,  spent 
5  cents  Friday,  earned  8  cents  Saturday,  and  put  7  cents 
in  the  missionary-box  on  Sunday.     How  much  of  his 
week's  earnings  had  he  left  ? 

5.  There  were  11  boys  at  play  in  the  yard,  when  5  of 
them  went  home,  2  went  off  to  play  with  some  other  boys, 
and  4  new  boys  came.  How  many  boys  were  there  in  the 
yard  at  last  ? 

6.  Frank  found  a  hen's  nest  with  9  eggs  in  it.   He  took 
out  3,  and  two  days  after  found  that  the  hens  had  laid  5 
more  eggs  in  the  nest.     He  then  took  6  out  of  the  nest. 
How  many  did  he  leave  in  the  nest  at  last  ? 

7.  John  has  17  cents.    He  lost  5,  spent  4,  earned  3, 
and  gave  away  6.     How  many  had  he  then  ? 

8.  A  man  has  agreed  to  work  9  hours.      How  many 
more  hours  has  he  to  work  after  he  has  worked  5  hours  ? 
9  less  5  is  how  many  ? 

9.  I  bought  an  orange  for  5  cents,  and  handed  the  gro- 
cer a  piece  of  money  worth  10  cents.     How  much  change 
must  he  give  me  ? 

10.  I  gave  a  boy  one  dime,  and  he  gave  me  a  glass  of 
chestnuts  worth  8  cents.    How  many  cents  should  he 
give  me  in  change  ?     8  and  how  many  make  10  ? 

11.  A  man  has  11  miles  to  ride.    How  many  more  has 
he  to  ride  after  he  has  ridden  6  ? 


4* 


78 


SUBTRACTION— EXERCISES   FOR 


MULTIPLICATION. 


.—^  teach  how  to  find  oat  the  product 
of  any  number  less  than  //  multiplied  by  any  num- 
ber less  than  //,  and  to  fix  the  results  in  memory  ; 
i.  e.,  to  learn  the  multiplication  table  to  70  times  7O. 

Method.  —  Teach  the  pupil  to  find  out  the  product  by  adding  the 
number  to  itself  the  requisite  number  of  times. 

First  Exercise.* 

1.  If  you  pick  a  cherry  and  put  it  in  your  hand,  and 
then  pick  another,  how  many  cherries  will  you  haye  ? 
How     many    times 

have  you  picked  1 
cherry  ?  Two  times 
1  cherry  are  how 
many  cherries  ? 

2.  1  4-  1  =  how 
many  ?     How  many 
times  1  are  1  -f  1  ? 
Two  times  1  are  how 
many  ? 

3.  If  you  pick  1 
cherry,      then     an- 
other, and  then  an- 
other,    how     many 
times  will  you  have 
picked    a     cherry  ? 

How  many  cherries  will  you  have  ?     3  times  1  cherry 
are  how  many  cherries? 

*  Multiplication  is  to  be  taught  as  based  on  addition.  Counters  and  the  Nu- 
meral frame  will  be  of  constant  service.  Explain  the  use  of  the  sign  x  ,  read- 
ing 3  x  4,  "  3  times  4,"  etc. 


PUPILS  READING  SIMPLE  WORDS.   79 

4.  1  +  14-1  =  how  many  ?     How  many  times  1  are 
1  -|- 1  + 1  ?     3  times  1  are  how  many  ? 

5.  If  your  mother  give  you  1  cent  each  day  for  4  days, 
how  many  times  will  she  have  given  you  1  cent  ?     How 
many  cents  will  you  have  ?     4  times  1  cent  are  how  many 
cents  ? 

6.  1  +  1  +  1  +  1  =  how  many  ?    How  many  times  1  are 
1  +  1  +  1  +  1?     4  times  1  are  how  many  ? 

7.  If  Jane  breaks  1  needle  each  day,  how  many  does 
she  break  in  a  week  (6  days)  ?   How  many  are  6  times  1  ? 

8.  The  sign  x  means  times,  and  we  read  3x2,  three 
times  two. 

9.  Head  4  x  1,  3  x  1,  5  x  2,  6  x  4.* 

10.  Read  3  x  2,  4  x  7,  5  x  6,  8  x  9,  7  x  4. 


*1= 

flxl= 

-f      1     1  

2x1  = 

1+1+1= 

3x1  = 

1+1+1+1= 

4x1  = 

1+1+1+1+1= 

5x1  = 

1+1+1+1+1+1= 

6x1  = 

1+1+1+1+1+1+1= 

7x1  = 

1+1+1+1+1+1+1+1— 

8x1  = 

l  +  l  +  l  +  l-t-l  +  l  +  l  +  l  +  l  = 

9x1  = 

1  +  1  +  1  +  1  +  1  +  1  +  1  +  1  +  1  +  1—      10x1  = 

111111111         10 

0 

12      3       456789       10       1 

4 

*  These  paragraphs  will  need  careful  explanation  before  the  pupil  is  required 
to  study  them.    Show  by  the  Numeral  Frame  what  is  meant  by  "•  3  times  1,"  etc. 

t  This  column  is  to  be  copied  by  the  pupil,  the  results  written,  and  the  whole 
thoroughly  committed  to  memory. 


80     MULTIPLICATION— EXERCI SES  FOR 


Second  Exercise. 

1.  There   are   2   cherries  in  each 
bunch,  and  2  bunches.     How  many 
times  2   cherries  are   there   on  the 
twig  ?  How  many  cherries  are  there  ? 
2  times  2    cherries  are   how   many 
cherries  ? 

2.  2  +  2=  how  many?  How  many  times  2  is  2  +  2? 
2x2=  how  many  ? 

3.  John  staid  out  of  school  2  days  to  visit  his  uncle,  2 
days  because  he  was  sick,  and  2  days  he  played  truant. 
How  many  times  did  he  stay  out  2  days  ?     How  many 
days  did  he  stay  out  in  all  ?  3  times  2  days  are  how  many 
days? 

4.  *  2  +  2  +  2  =  how  many  ?    How  many  times  2  are 
2  +  2  +  2  ?    3x2  are  how  many? 

5.  Jane  found  2  eggs  on  Monday,  2  on  Tuesday,  2  on 
Wednesday,  and  2  on  Thursday.     How  many  times  did 
she  find  2  eggs  ?    How  many  did  she  find  in  all  ?    4  times 
2  eggs  are  how  many  eggs  ? 

6.  *2+2+2+2=  how  many ?     How  many  times  2  is 
2  +  2  +  2  +  2?     4x2=  how  many? 

7.  4  times  2  are  how  many  ?     If  4  times  2  are  8,  how 
many  are  5  times  2  ?     How  many  2's  must  you  take  with 
4  times  2,  or  8,  to  make  5  times  2  ? 


*  The  pupil  is  expected  to  perform  the  addition,  thus  keeping  up  a  drill  in 
adding. 


PUPILS  READING  SIMPLE    WORDS,      81 


8.  6  times  2  are  12.     How  many  are  7  times  2?     How 
many  2's  must  you  put  with  6  times  2,  or  12,  to  make  7 
times  2  ? 

9.  8  times  2  are  16.     How  many  are  9  times  2  ?* 


2  +  2  = 

2+2+2= 

2+2+2+2= 

2+2+2+2+2= 

2+2+2+2+2+2= 

2+2+2+2+2+2+2= 

2+2+2+2+2+2+2+2= 

2+2+2+2+2+2+2+2+2= 

2+2+2+2+2+2+2+2+2+2= 


2      2 

2      3 


2 
4 


2 
5 


2 

6 


2 

7 


2      2 
8       9 


2 
10 


2x2: 

3X2: 

4x2: 
5x2: 

6X2: 

7x2: 

8x2; 
9x2: 

10X2: 

0 
2 


1 

2 


2 
2 


Third  Exercise. 

1.  Frank    spent    3    cents 
each  day  in  the  week  except 
Sunday.     How  many   times 
did  he  spend  3  cents  ?    How 
many  cents  did  he  spend  in 

all?      6  times  3  cents  are  how  many  cents? 

2.  3 +  3 +  3 +  3 +  3 +  3=  how  many?   How  many  times 
3  is  3  +  3  +  3  +  3  +  3  +  3?     6x3  are  how  many? 


*  Special  pains  should  be  taken  to  have  the  pupil  see  the  process  as  succes- 
sive additions  of  the  game  number,  so  that  if  he  knows  what  7  x  6  is,  he  can  tell 
What  8x6  is,  etc. 


82     MULTIPLICATION.— EXERCISES  FOR 

3.  George  reads  3  pages  eacli  day  of  the  week.    How 
many  times  3  pages  does  he  read  ?   How  many  are  7x3? 

4.  3 +3  +  3  +  3  +  3  +  3  +  3=  how  many?     How  many 
times  3  are  3  +  3  +  3  +  3  +  3  +  3  +  3?    7  times  3  are  how 
many  ? 

5.  James  goes  a  fishing  each  day  for  4  days  and  catches 
0  fish  each  day.     How  many  does  he  catch  in  all  ?     How 
many  are  4  times  0  ?     5  times  0  ? 

6.  4  times  3  are  12.    How  many  more  3's  are  5  times 
3  than  4  times  3  ?     How  many  are  5  times  3  ? 

7.  6  times  3  are  18.     How  many  are  7  times  3  ? 

8.  8  x  3=24.     How  many  are  9x3?     10  x  3  ? 

9.  If  you  know  how  many  5  times  3  are,  how  can  you 
tell  from  this  how  many  6  times  3  are  ? 


3+3+3— 

3+3+3+3= 

3+3+3+3+3= 

3+3+3+3+3+3= 

3  +  3  +  3  +  3++33  +  3=  ' 

3+3+3+3+3+3+3+3= 

3+3+3+3+3+3+3+3+3= 

3+3+3+3+3+3+3+3+3+3= 


3 
3 

2 

7 


3   3 

£  A 

2 
0 


33333 

87458 


1 
4 


3 

5 


1 
8 


2 
9 


0 
3 


•i 

o 

X 

q  

4 

X 

q  

5 

X 

3  = 

6 

X 

3  = 

7 

X 

3  = 

8 

X 

q  

9 

X 

q  

10 

X 

3  = 

0       3 

3 

5       7 

10 

1 

2 

3 

3 

3 

3 

PUPILS  READING   SIMPLE    WORDS.       S3 


Fourth  Exercise. 


1.  How  many  legs  has  1  lamb  ?     Five  lambs  have  how 
many  times  as  many  legs  as  1  lamb  ?    How  many  legs 
have  5  lambs? 

2.  How  many  legs  have  4  lambs  ?    How  many  times  as 
many  legs  as  1  lamb  ?     How  many  are  4  times  4  ? 

3.  How  many  legs  have  6  lambs  ?    How  many  times 
as  many  legs  as  1  lamb  ?     Six  times  4  are  how  many  ? 

4.  Seven  lambs  have  how  many  times  as  many  legs  as 
1  lamb  ?     7  lambs  have  how  many  legs?     7x4= how 
many  ? 

5.  James  bought  8  oranges  and  gave  4  cents  for  each. 
How  many  times  4  cents  did  he  give  for  all  his  oranges  ? 
How  many  are  8  times  4  ? 

6.  4  -|_  4  +  4  +  4  _|-  4  _|_  4  _{_  4  +  4  +  4=  how  many  ?    How 
many  times  4  are  4  +  4  +  4  +  4  +  4  +  4  +  4  +  4  +  4  ?     9x4 
=  how  many  ? 

7.  3  times  4  are  12.     How  many  more  4's  are  4  times  4 
than  3  times  4  ?     How  many  are  4x4? 

8.5x4=20.  How  many  are  6  x 4 ?  7x4?  8x4? 
9x4?  10x4?  How  many  more  do  you  take  each 
time  ? 


84     MULTIPLICATION.— EXERCISES  FOR 


4+4+4+4= 

4x4= 

4+4+4+4+4= 

5x4= 

4+4+4+4+4+4= 

6x4= 

4+4+4+4+4+4+4= 

7x4= 

4+4+4+4+4+4+4+4= 

8x4= 

4+4+4+4+4+4+4+4+4= 

9x4= 

4+4+4+4+4+4+4+4+4+4= 

10x4= 

4 

444444333 

2 

5 

7468   10    9374 

7 

1 
8 

3 
6 

2 

8 

3 
5 

1 
5 

3 

8 

0 
4 

1 
4 

2 
4 

3 
1 

4 
1 

Fifth    Exercise. 


1 .  How  many  points  has  one  star  ?    How  many  have  5 
stars?     How  many  have  6  stars?     7  stars?     8  stars? 
9  stars  ?     10  stars  ? 

2.  Six  stars  have  how  many  times  as  many  points  as  1 
star  ?     Seven  stars  have  how  many  times  as  many  points 
as  1  star  ?     Eight  stars  have  how  many  times  as  many 
points  as  1  star  ? 

3.  5  +  5  +  5  +  5  +  5  +  5  are  how  many  times  5  ?   6  times 
5  are  how  many  ? 


PUPILSREADING   SIMPLE    WORDS.       85 


4.  5  +  5  +  5  +  5  +  5  +  54-5  +  5  are  how  many  times  5  ? 
8  times  5  are  how  many  ? 

5.  If  John  earns  5  cents  each  day,  how  many  cents  can 
he  earn  in  G  days  ?     How  many  times  as  many  can  he 
earn   in    G   days   as  in   1   day?     Six   times   5   are  how 
many  ? 

G.  How  many  cents  can  John  earn  in  10  days,  if  he  can 
earn  5  cents  in  1  day  ?  How  many  times  as  many  cents 
can  he  earn  in  10  days  as  in  1  day  ? 

7.  3  times  5  are  how  many  ?  How  many  more  are  4 
times  5  ?  How  many  are  4  times  5  ?  7  times  5  ?  8 
times  5  ?  9  times  5  ?  10  times  5  ?  How  many  more  5's 
do  you  take  each  time  ? 


5+5+5+5+5= 
5+5+5+5+5+5= 
5+5+5+5+5+5+5= 
5+5+5+5+5+5+5+5= 
5+5+5+5+5+5+5+5+5= 

5x5  = 
6x5  = 

7x5  = 
8x5  = 
9x5  = 

5 

+5+5+5+5+5+5+5+5+5= 

10x5  = 

5 

5 

5 

5 

5 

5 

0 

1 

2   3 

4 

5 

5 

6 

7 

8 

9 

10 

5 

5 

5   5 

5 

5 

4 

3 

2 

3 

4 

5 

1 

0 

4   4 

4 

4 

7 

7 

8 

8 

8 

8 

8 

8 

6   9 

10 

4 

86     MULTIPLICATION.— EXERCISES  FOR 


Sixth  Exercise. 

1.  How  many  petals* 
has  one  lily?   How  many 
times    as    many  have   7 
lilies  ?     How  many  pet- 
als have  7  lilies  ?    7  times 
6  are  how  many  ? 

2.  If  1  lily  has  6  petals, 
how  many  petals  have  8 
lilies?     How  many  have 
9  lilies  ?   How  many  times 
6  petals  have  10   lilies? 
How  many  petals  have  10 
lilies  ? 

3.  If  James  "buys  6  oranges  for  6  cents  apiece,  how 
many  cents  must  he  pay  for  all  ? 

4.  How  many  times  as  much  must  James  pay  for  9 
oranges  as  for  1  ?     How  much  must  he  pay  for  9  oranges 
if  1  orange  is  worth  6  cents  ? 

5.  6  +  6  +  6  +  6  +  6  +  6  are  how  many  times  6  ?   6  times 
6  are  how  many  ? 

6.  If  each  of  8  boys  has  6  nuts,  how  many  have  they 
all  ?     How  many  times  6  nuts  have  they  ?     8  times  6 
nuts  are  how  many  nuts  ? 

7.  2  times  6  are  12.    How  many  more  6's  must  you 
take  to  make  3  times  6  ?     How  many  are  3  times  6  ? 
How  many   more   are   4  times   6  ?     How   many  are  4 
times  6  ? 


*  Teacher  be  careful  to  explain  the  meaning  of  this  word,  and  teach  the 
pupil  how  to  pronounce  it. 


P  UPILS  READING   SIMPLE    WORDS.      87 


8.  5  x  6  =  30.     How  many  are  6  x  6  ?     7x6? 

9.  8  x  6  =  48.     How  many  are  9  x  6  ?     10  x  6  ? 

10.  When  you  know  how  many  7  times  6  are,  how 
do  you  find  out  how  many  8  times  6  are  ? 


6+6+6+6+6+6= 

6+6+6+6+6+6+6= 

6+6+6+6+6+6+6+6= 

6+6+6+6+6+6+6+6+6= 

6+6+6+6+6+6+6+6+6+6= 


666660 
9   10   7686 


123 

666 


6x6: 
7x6; 
8x6: 
9x6: 

10X6: 


4 
6 


5 
6 


6 
6 


Seventh  Exercise. 

1.  There  are  7  days  in  one  week.    How  many  times 
as  many  days  are  there  in  4  weeks  ?     How  many  days  in 
4  weeks  ?     How  many  days  in  2  weeks  ?    How  many  in 
6  weeks  ? 

2.  How  many  days  are  there  in  8  weeks?    "Why?* 
How  many  days  in  9  weeks  ?    Why  ?    How  many  days 
in  10  weeks?    Why? 

3.  If  Jane  finds  7  eggs  each  day,  how  many  will  she 
find  in  6  days  ?     Why  ? 

4.  7  +  7  =  how  many  ?     7  +  7  are  how  many  times  7  ? 
2  times  7  are  how  many  ? 


*  The  answer  should  be,  "  Because  there  are  8  times  as  many  days  in  8 
weeks  as  there  are  in  1  week,  and  8  times  7  are  56." 


MULTIPLICATION.— EXERCISES   FOR 


*  * 

*  *  *  ** 

**  *  *  * 

***  ** 


5.  How  many  times  7  stars 
are  there  here?    How  many 
stars  in  a  row  from  left  to 
right?       How    many    rows? 
How   many   times   as   many 
stars  are  there  in  8  rows  as 
there  are  in  1  row  ?     8  times 
7  stars  are  how  many  stars  ? 

6.  How  many  stars  are  there 
in  7  of  the  rows  from  left  to 
right  ?     Why  ? 

7.  If  3  times  7  are  21,  how  many  are  4  times  7 

8.  If  5  times  7  are  35,  how  many  are  6  times  7 

9.  How  many  more  are  8  times  7  than  7  times 
10.  4  x  7=28.     How  many  are  5  x  7  ?     6x7? 


* 
* 
* 


***** 
***** 

***** 


* 
* 

* 


* 
* 

* 


7-? 

7 


x7? 


7+7+7+7+7+7+7= 
7+7+7+7+7+7+7+7= 
7+7+7+7+7+7+7+7+7= 
7+7+7+7+7+7+7+7+7+7= 


7x7: 
8x7: 
9x7: 

10X7: 


7 
8 


7   7 
9   7 


7 
10 


0   1 

7   7 


2   3 

7   7 


4   5 

7   7 


6 

7 


7 

7 


234567875463 
345674375463 


PUPILS  READING  SIMPLE  WORDS.   89 


Eighth  Exercise. 


1.  How  many  o's  are  there  in 
a  row?     How  many  e's?     How 
many  b's  ?     How  many  letters  in 
each   row  ?      How   many  rows  ? 
How   many  times    8   letters  are 
there  ?   How  many  letters  in  all  ? 
9  times  8  letters  are  how  many 
letters  ? 

2.  If  we  write  a  row  of  8  m's 
under  the  g's,  how  many  rows  of 


oooooooo 

eeeeeeee 

aaaaaaaa 

i  i  i  i  i  i  i  i 

11  n  u  11  11  11  11  11 

cccccccc 

bbbbbbbb 

ffffffff 

gggggggg 


10 


letters  will  there  be  ?     How  many  times  8  letters  ? 
times  8  letters  are  how  many  letters  ? 

3.  If  we  cover  up  the  row  of  g's,  how  many  rows  of 
letters  will    there    be?      How  many  times  8  letters? 
8x8  =  how  many  ? 

4.  If  there  are  9  boys,  and  each  boy  has  8  cents,  how 
many  times  8  cents  have  they  all  ?     How  many  cents 
have  they  all  ?     9  times  8  are  how  many  ? 

5.  If  there  are  10  girls  in  the  class,  and  each  girl  has  8 
buttons  on  her  dress,  how  many  buttons  are  there  on  all 
their  dresses?     How  many  times  8  buttons  are  there? 
10  times  8  are  how  many  ? 

6.  2  x  8=16.     How  many  are  3x8?    4x8?    5x8? 
6x8?     7x8? 


8+8+8+8+8+8+8+8= 
8+8+8+8+8+8+8+8+8= 
8+8+8+8+8+8+8+8+8+8= 

888012345 
10     89888888 

8x8  = 
9x8  = 
10x8  = 

678 
888 

90     MULTIPLICATION.— EXERCI SES  FOR 


Ninth  Exercise. 

1.  How  many  branches  lias 
this  plant  ?    How  many  leaves 
on  each  branch  ?     How  many 
times  9  leaves  are  there  on  the 
plant  ?     10  times  9  leaves  are 
how  many  leaves  ? 

2.  If  you  were  to  break  off 
the  lowest  branch,  how  many 
branches  would  be  left  ?   How 
many  leaves  ?      9x9  =  how 
many  ? 

3.  If  you  were  to  break  off 

two  of  the  lower  branches,  how  many  branches  would  re- 
main ?     How  many  leaves  ?     8x9=  how  many  ? 

4.  If  you  were  to  break  off  3  of  the  branches,  how  many 
branches  would  remain  ?    How  many  leaves  ?     7  times  9 
are  how  many  ? 

5.  How  many  fingers  has  a  boy  on  both  hands,  with  his 
thumbs  ?   How  many  have  10  boys  ?   10  tens  make  what  ? 

6.  How  many  fingers  have  8  boys  ?     7  boys  ?     6  boys  ? 
9  boys? 

7.  If  a  boy  earns  10 
cents  each  day,  how  many 
cents  does  he  earn  in  2 
days  ?   3  days  ?    6  days  ? 
8  days?  10  days?  10x10 
=  how  many  ? 


8.  ::X9  =  18.   3x9=?  4x9=?  5x9=45.   6x9=? 
7x9=?     3x9=? 


PUPILS   READING   SIMPLE    WORDS.       91 


9 
9 


9x9  = 

9  +  9  +  9  +  9  +  9  +  9  +  9  +  9  +  9  +  9=      10x9  = 

10  +  10  +  10  +  10  +  10  +  10  +  10  +  10  +  10  +  10  = 

10x10  = 

90123456789 
10   9999999999 


10        01234567 

10      10     10     10     10     10     10     10     10      10      10 


10 
_9 

10 
10 


Tenth  Exercise.* 

1.  Here  are  two  piles 
of  money.    In  the  upper 
there  are  5  3-cent  pieces. 
How  many  cents  are  in 
it?     5  times  3  are  how 
many  ?    In  the  lower  are 
3   5 -cent  pieces.      How 
many   cents   in   it  ?     3 
times  5  are  how  many  ? 
In  which  pile  is  there  the 
most  money  ?    5  times  3 
is  the  same  as  what  ? 

2.  James  earned  3  cents  each  day  for  4  clays.     How 
many  cents  had  he  ?     John  earned  4  cents  each  day  for  3 
days.     How  many  cents  had  he?     Which  had  the  more? 

*  The  purpose  of  this  exercise  is  to  teach  that  the  factors  may  be  exchanged 
without  affecting  the  product ;  i.  e.,  that  4  times  3  is  the  same  as  3  times  4,  etc 
This  truth  should  be  amply  illustrated  by  oral  exercises  akin  to  these  here 
given,  before  the  pupil  is  required  to  study  these. 


92     MULTIPLICATION.— EXERCISES   FOR 

3.  4  times  3  are  how  many  ?   3  times  4  are  how  many  ? 
Which  is  the  most,  3  times  4  or  4  times  3  ? 

4.  Mary  has  10  5-cent  pieces  and  Jane  has  5  10-cent 
pieces.    Which  has  the  most  ?    Why  ? 

5.  If  you  count  the  rows 

Jf 
of  stars  from  left  to   right, 

how  many  stars  are  there  in  ** 

a  row  ?     How  many  rows  of          4f  "fc  "fc  *jt 

7  stars  each  ?     How  many          -fr  ^T  +C 
stars  ?   If  you  count  the  rows 

of  stars  down  the  page,  how 
many  stars  are  there  in  a  row  ? 

How  many  rows  of  8  stars          -k  -k  4f  -k  «k  4r  ^r 

each?      8  times  7  are  how 

many  ?     7  times  8  are  how  many  ?    Which  is  the  most, 

8  times  7  or  7  times  8  ? 

6.  5  times  3  are  how  many  ?    Then  how  many  are  3 
times  5  ?     Why  ?  * 

7.  6  times  4  are  how  manv?    Then  4  times  6  are  how 

it 

many  ?    Why  ? 

8.  7  times  6  are  how  many  ?    Then  6  times  7  are  how 
many  ?     Why  ? 


*  111  these  exercises  it  is  to  be  observed  that  the  first  product  has  been 
learned  already,  and  from  it  the  second  is  to  be  inferred.  Thus,  they  have 
learned  that  5  times  3  are  15,  and  are  hence  to  infer  that  3  times  5  are  15.  The 
form  of  answer  should  be  something  like  this :  "  Because  5  times  3  are  15,  and 
3  times  5  are  just  as  many  as  5  times  3."  This  important  truth  should  be  made 
perfectly  familiar ;  it  lessens  the  work  of  learning  the  multiplication  just  one- 
half. 


P  UPILS   READING    SIMPLE     WORDS.     93 


*lx2  = 

,  hence  2x1  = 

Ix   8  = 

,  hence    8x1  = 

2x2= 

2x   8  = 

,  hence    8x2  = 

1x3  = 

,  hence  3x1  = 

3x    8  = 

,  hence    8x3  = 

2x3  = 

,  hence  3x2  = 

4x    8  = 

,  hence    8  x  4= 

3x3  = 

5x8  = 

,  hence    8x5  = 

1x4= 

,  hence  4x1  = 

6x8  = 

,  hence    8x6  = 

2x4= 

,  hence  4x2  = 

7x    8  = 

,  hence    8x7  = 

3x4= 

,  hence  4x3  = 

8 

x8= 

4x4= 

1x9  = 

,  hence    9x1  = 

1  x5  = 

,  hence  5x1  = 

2x    9  = 

,  hence    9x2= 

2x5  = 

,  hence  5x2= 

3x9  = 

,  hence    9x3  = 

3x5  = 

,  hence  5x3  = 

4x    9  = 

,  hence    9x4  = 

4x5  = 

,  hence  5x4= 

5x    9  = 

,  hence    9x5  = 

5  x5  = 

6x9  = 

,  hence    9x6  = 

1x6  = 

,  hence  6x1  = 

7x    9  = 

,  hence    9x7  = 

2x6  = 

,  hence  6x2  = 

8x    9  = 

,  hence    9  x  8= 

3x6  = 

,  hence  6x3  = 

9 

x9  = 

4x6  = 

,  hence  6x4= 

1x10  = 

,  hence  10  x  1  = 

5x6  = 

,  hence  6x5  = 

2x10= 

,  hence  10  x  2= 

6x6  = 

3x10= 

,  hence  10  x  3  = 

1x7= 

,  hence  7x1  = 

4x10= 

,  hence  10  x  4= 

2x7= 

,  hence  7x2  = 

5x10= 

,  hence  10  x  5  = 

3x7  = 

,  hence  7x3  = 

6x10  = 

,  hence  10  x  6  = 

4x7  = 

,  hence  7x4= 

7x10  = 

,  henee  10  x  7  = 

5x7  = 

,  hence  7x5  = 

8x10  = 

,  hence  10  x  8= 

6x7  = 

,  hence  7x6  = 

9x10  = 

,  hence  10  x  9  = 

IV   ..   W  

10x10  = 

*  This  table  affords  exercises  like  the  preceding,  and  should  be  used  to  fa- 
miliarize the  idea  that  the  order  of  the  factors  is  indifferent,  and  also  as  an  ex- 
ercise to  aid  in  fixing  the  products  in  mind.  Pupils  should  copy  it  and  fill  it 
out ;  they  should  recite  it  individually  and  in  concert. 


94     MULTIPLICATION— EXERCISE  S   FOR 

Eleventh  Exercise. 

1.  *  6  +  6  +  6  +  6  are  how  many  times  6  ?     How  many 
are  4  times  6  ? 

2.  3+3+3+3+3+3+3+3   are  how  many?     How 
many  times  3  ?     8  times  3  are  how  many  ? 


1  +  1  =    ,  hence  2  x   1  = 
2+   2=   ,  hence  2  x   2  = 
3  +  3  =    ,  hence  2  x   3  = 
4+   4=    ,  hence  2  x    4= 

6+   6  = 

7+   7= 

O     i        O 
0+     0  = 

9+   9  = 

,  hence  2  x   6= 
,  hence  2  x    7  = 
,  hence  2  x   8  = 
,  hence  2  x   9  = 

5+  5=   ,  hence 

2x   5  = 

10  +  10  = 

,  hence  2  xlO= 

1  - 

h    1 

+    1=       , 

hence 

3 

x 

1 

___ 

2  - 

h    2 

+    2  =       , 

hence 

3 

x 

2 

— 

3  - 

h    3 

+    3  =       , 

hence 

3 

X 

3 

—  • 

4- 

h    4 

+    4=       , 

hence 

3 

X 

4 

— 

5  - 

h    5 

1                '                   ? 

hence 

3 

X 

5 

_  . 

6  - 

h    6 

+    6=       , 

hence  3 

X 

6 

:= 

7H 

h    7 

+    7=       , 

hence 

3 

X 

7 

—  • 

8  H 

-    8 

+    8  =       , 

hence 

3 

X 

8 

—  • 

9H 

h    9 

+    9=       , 

hence 

3 

X 

9 

—  • 

10  H 

-10 

+  10=       , 

hence 

3 

X 

10 

=: 

3.     1  +  1  + 

1  +  1 

.=     ,  hence 

4x1 

—  • 

2  +  2  +  2  +  2=     ,  hence  4x2= 

3  +  3  +  3  +  3=     ,  hence  4x3  = 

4  +  4  +  4  +  4=     ,  hence  4x4= 

Let  the  pupil  copy  this  on  his  slate  and  fill  it  out  to  4 
times  10,  and  write  in  all  the  results.  So  also  of  the 
following : 

*  The  pupil  is  expected  to  add  the  6's,  and  thus  find  out  the  answer.  It  is 
designed  that  exercise  in  addition  as  well  as  instruction  in  multiplication  be 
secured. 


PUPILS   READING   SIMPLE    WORDS.       95 


4.  1  +  1  +  1  +  1  +  1=     ,  l^nce  5x1  = 

2  +  2  +  2  +  2  +  2=     ,  hence  5x2=     ,  etc. 

5.  1  +  1  +  1  +  1  +  1  +  1=     ,  hence  6x1  = 

2  +  2  +  2  +  2  +  2  +  2=     ,  hence  6x2=     ,  etc. 

6.  1  +  1  +  1  +  1  +  1  +  1  +  1=     ,  hence  7x1  = 

2  +  2  +  2  +  2  +  2  +  2  +  2=     ,  hence  7x2=     ,  etc. 

7.  14_1_I_1_I_1  +  1  +  1+1  +  1=     ,  hence  8x1  = 

2+2  +  2  +  2  +  2  +  2  +  2  +  2=     ,  hence  8x2=     ,  etc. 

8.  1  +  1  +  1  +  1  +  1  +  1  +  1  +  1  +  1=  ,hence9xl  = 

2  +  2  +  2  +  2  +  2  +  2  +  2  +  2  +  2=  ,  hence  9x2=  ,etc. 

9. 

1  +  1  +  1  +  1  +  1+1  +  1+1+1  +  1=  ,  hence  10x1  = 

2  +  2  +  2  +  2  +  2  +  2+2  +  2  +  2  +  2=  ,  hence  10x2=  ,etc. 


Twelfth  Exercise. 

1.  Eepeat  the  2's  of  the  multiplica- 
tion table  5  times,  thus :  * 

1  time  2  is      . 

2  times  2  are . 

3  times  2  are ,  etc. 

2.  Eepeat  the  2's  5  times  in  this 
way: 

2  times  1  are . 

2  times  2  are . 

2  times  3  are .  etc. 


*  Teacher  show  the  child  how  to  keep  his  tally  by  marks  as  he  says  the  exer- 
cise over,  so  as  to  know  when  he  has  been  over  it  five  times. 


96     M UL  TIP  LI  CAT  ION.— EXERCISES  FOR 

3.  Repeat  the  3's  5  times  thus : 

1  time  3  is      .  *         *         *        *         # 

2  times  3  are .  *  #     *  #     *  *     ##     *  * 

3  times  3  are ,  etc. 

4.  Repeat  the  3's  5  times  thus" : 

3  times  1  are .  *  *  *  * 

O     J_!  O  *  *  * 

3  times  2  are . 

3  times  3  are ,  etc. 

5.  Answer  the  following  5  times : 

2x3?  4x2?  2x7?  7x2?  3x1?  6x3?  5x3? 
3x5?  4x3?  3x4?  2x8?  8x2?  7x3?  2x7? 
1x2?  1x3?  5x2?  3x5?  9x3?  9x2?  3x9? 

6.  If  1  orange  costs  4  cents,  how  many  cents  will  3 
oranges  cost  ? 

If  1  orange  cost  4  cents,  3  oranges  will  cost  3  times  4  cents,  or 
12  cents. 

7.  If  1  pencil  costs  5  cents,  how  many  cents  will  3  pen- 
cils cost  ? 

8.  If  a  boy  learns  2  lessons  each  day,  how  many  lessons 
does  he  learn  in  6  days  ?    In  9  days  ? 

9.  There  are  7  days  in  one  week.    How  many  days  are 
there  in  2  weeks  ?    In  3  weeks  ? 


Thirteenth  Exercise. 


1.  Repeat  the  4's  5  times  in  each  of  the  two  ways,  thus: 
1  time  4  is     .       4  times  1  are 


2  times  4  are 

3  times  4  are 
etc.,  etc. 


4  times  2  are 
4  times  3  are 
etc.,  etc. 


P  UPILS  READING   SIMPLE    WORDS.      97 
2.  Repeat  the  5's  5  times  in  each  of  the  two  ways,  thus: 


1  time  5  is 

2  times  5  are 

3  times  5  are 
etc.,  etc. 


5  times  1  are 
5  times  2  are 
5  times  3  are 
etc.,  etc. 


3.  Repeat  the  6's  5  times  in  each  of  the  two  ways,  thus : 


1  time      6  is 

2  times  6  are 

3  times  6  are 
etc.,  etc. 


G  times  1  are 
6  times  2  are 
6  times  3  are 
etc.,  etc« 


4.  Copy  the  following  on  your  slates,  multiply,  and 
write  the  results  underneath  : 
647896785469 

4  7  5    6   6   ?  A  JL  _?_  A  JL  JL 

759       6645     10      2       665 
6       7      4 


5.  James  worked  7  hours  for  5  cents  an  hour.    How 
much  did  he  earn  ? 

6.  John  worked  6  hours  for  4  cents  an  hour,  and  Henry 
worked  4  hours  for  6  cents  an  hour.    Which  earned  the 
most? 

7.  Jane  bought  7  oranges  for  6  cents  each.   How  much 
did  they  cost  ? 

8.  Mary  bought  4  spools  of  thread  for  5  cents  a  spool, 
and  gave  the  clerk  25  cents.     How  much  change  should 
he  give  her  ?     How  much  did  her  thread  cost  ?     25  is 
how  much  more  than  20  ? 


98    MULTIPLICATION.— EXERCISES  FOR 


Fourteenth  Exercise. 


1.  Repeat  the  7's  5  times  in  each  of  the  two  ways,  thus : 


1  time  7  is 

2  times  7  are 
etc.,  etc. 


7  times  1  are 
7  times  2  are 
etc.,  etc. 


Repeat  the  8's  5  times  in  each  of  the  two  ways,  thus : 
1  time  8  is     .       8  times  1  are 


2  times  8  are 
etc.,  etc. 


8  times  2  are 
etc.,  etc. 


3.  Answer  the  following  5  times : 

8x7?  8x9?  6x8?  7x6?  8x6?  9x8?  9x7? 
7x9?  6x9?  9x6?  7x7?  8x8?  9x9?  7x5? 
7x4?  8x3?  3x8?  6x3?  4x6?  3x7?  3x9? 

4.  If  7  white  hens  have  8  chickens  each,  and  8  black 
hens  have  7  chickens  each,  which  have  the  most  chickens, 
the  white  hens  or  the  black  hens  ?    Why  ? 

5.  John  earns  6  cents  an  hour  and  works  7  hours,  and 
Henry  earns  7  cents  an  hour  and  works  6  hours.    Which 
earns  the  most  money  ? 

6.  Which  costs  the  most,  8  oranges  at  9  cents  each,  or 
9  oranges  at  8  cents  each  ?    Why  ? 

7.  In  the  first  column  there 
are  4  words,  with  7  letters 
in   each   word,  and  in   the 
second  are  7  words,  with  4 
letters  in   each    word.      In 
which  column  are  there  the 
most  letters  ?    Why  ? 


answers 
s  c  h  o  1  a  r 
f  o  1 1  o  w  s 
chicken 


late 
goes 
sail 
coat 
find 
snow 
rain 


PUPILS   READING  SIMPLE    WORDS.       99 


Fifteenth  Exercise. 

1.  Repeat  the  9's  5  times  in  each  of  the  two  ways,  thus: 

1  time  9  is      .       9  times  1  are . 

2  times  9  are .        9  times  2  are  -     -. 

etc.,  etc.  etc.,  etc. 


2.  Repeat  the  10's  5  times  in  each  of  the  twro  ways,  thus : 

10  times  1  are  -     -. 

10  times  2  are . 

etc.,  etc. 


1  time  10  is 

2  times  10  are 
etc.,  etc. 


3.    Answer  the  following  5   times.     Write  them  on 
your  slates  in  the  same  way  as  those  on  page  97. 

9x3?4x    9?   10x7?    8x9?    6x9?    7x9?    9x6? 
10x3?3xlO?     9x8?    9x6?    9x7?    3x9?    1x9? 


4.  Answer  the  following  : 

3x5  = 

3x7  = 

2x2 

7x8  = 

3x2  = 

3x3 

6x7  = 

5x8  = 

4x4 

9x8  = 

9x4  = 

5x5 

4x7  = 

9x3  = 

6x6 

7x5  = 

4x9  = 

7x7 

6x9  = 

3x9  = 

8x8 

10  x  8  = 

2x8  = 

9x9 

5x7  = 

3x8  = 

10  x  10 

7x6  = 

10  x    4  = 

1x1 

9x6  = 

3  x  10  = 

5x0 

8x7  = 

10  x  10  = 

0x3 

100     MULTIPLICATION— EXERCISES  FOR 


* 
*  * 


* 


* 
*  * 


Sixteenth  Exercise. 

1.  How  many  times  must  yon  make 

3  stars  to  have  12  stars  ?     How  many 
times  3  is  12  ?   4  times  3  are  how  many  ? 

2.  How  many  times  must  you  make    ////  ////  ////  //// 

4  marks  to  have  20  marks  ?   How  many 
times  4  is  20  ?   5  times  4  are  how  many  ? 

3.  Three  times  what  number  makes  12  ?    Three  times 
what  number  makes  18  ? 

4.  4  times  what  number  makes  20  ? 
5  times  what  number  makes  30  ? 

7  times  what  number  makes  21  ? 

8  times  what  number  makes  56  ? 

5.  Copy  the  following  table  on  your  slates  and  fill  it  out  :* 


2x      =  2 

3  x      =21 

4x 

=  20 

2x      =  6 

3x      =15 

4x 

=  16 

2x      =  8 

3x      =18 

4x 

=  4 

2x     =  4 

3x      =12 

4x 

=  12 

2x      =10 

3x      =  3 

4x 

=24 

2x      =14 

3x      =  9 

4x 

=40 

2x      =20 

3x      =27 

4x 

Q 

2x      =18 

3x      =  6 

4x 

=  36 

2x      =16 

3x      =30 

4x 

=  28 

2x      =12 

3x      =24 

4x 

=32 

6.  How  many  times  5  does  it  take      *  * 
to  make   15  ?      How  many  5's  are 
there  in  15  ? 

•f*    *i»          f*    T* 

*         * 

7.  How  many  times  6  does  it  take  to  make 
many  67s  in  24  ? 

24  ?    How 

*  The  teacher  may  need  to  explain  how  it  is  to  be  done. 


PUPILS  READING  SIMPLE   WORDS.     101 


Seventeenth  Exercise. 

1.  How  many  cents  do  6 
5  cent  pieces  make  ?     How 
many  5-cent  pieces  does  it 
take  to  make  30  cents  ?     6 
times  5  are  how  many  ?     6 
times  what  number  makes 
30? 

2.  How  many  cher- 
ries are  there  in  the 
picture  ?    How  many 
bunches?  How  many 
in   each  bunch?      7 
times  what    number 
makes  42  ? 

3.  Copy  the  following  table  on  your  slates  and  fill  it  out : 


5  x   =15 

6x   =18 

7  x   =28 

5x   =10 

6x   =12 

7x   =14 

5x   =20 

6x   =42 

7x   =35 

5x   =35 

6x   =48 

7x   =63 

5x   =50 

6x   =24 

7x   =70 

5  x   =45 

6x   =30 

7x   =42 

5x   =  5 

6x   =  6 

7x   =21 

5x   =25 

6x  =54 

7x  =  7 

5x   =30 

6x   =36 

7x   =56 

5x   =40 

6x   =60 

7x   =49 

4.  How  many  times  must  John  bring  in  4  eg^s  at  a 
time,  in  order  to  bring  in  24  eggs  ?  How  many  times  4 
does  it  take  to  make  24  ? 


102     MULTIPLICATION.— EXERCISES   FOR 

5.  If  Henry  earns  5  cents  an  hour,  how  many  cents 
will  he  earn  in  7  hours  ? 

6.  If  Henry  earns  5  cents  an  hour,  how  many  hours 
will  it  take  him  to  earn  35  cents?     Why  ?    Answer.  Be- 
cause 7  times  5  are  35. 


Eighteenth  Exercise. 

1.  Here  are  two  squares  of 
black  glass,  with  9  flakes  of 
snow  on  each.     How   many 
squares  would  it  take  to  have 
72  flakes  of  snow  ?     8  times 
9  are  how  many  ? 

2.  A  class   of  boys  had  90  fingers,  including  their 
thumbs.     How  many  boys  were  there  in  the  class.     How 
many  10's  does  it  take  to  make  90  ?    9  times  10  are  how 
many  ? 

3.  Copy  the  following  table  on  your  slates  and  fill  it  out : 


8x 

=16 

9x 

=36 

10  x 

=  40 

8x 

=40 

9x 

=27 

10  x 

=  70 

8x 

=24 

9x 

=  18 

10  x 

=  90 

8x 

=  56 

9x 

=45 

10  x 

=  30 

8x 

=  64 

9x 

=  63 

10  x 

=  10 

8x 

=  8 

9x 

=  81 

10  x 

=  20 

8x 

=  72 

9x 

=  9 

10  x 

=  100 

8x 

=  32 

9x 

=  54 

10  x 

=  50 

8x 

=  80 

9x 

=  90 

10  x 

=  80 

8x 

=48 

9x 

=  72 

10  x 

=  60 

PUPILS  READING  SIMPLE    WORDS.   103 


4.  If  John  catches  7  fishes 
each  day,  how  long  will  it  take 
him  to  catch  42  fishes  ?   6  times 
7  are  how  many  ? 

5.  If  Moses  lays  hy  10  cents 
a  week,  how  many  weeks  will  it 
take  him  to  lay  by  one  dollar, 
or  100  cents  ?     How  many  tens 
does  it  take  to  make  100  ? 


Definition  Exercise. 

1.  If  one    currant 
"bush    produces   two 
quarts    of   currants, 
how  many  quarts  will 
3  currant  bushes  pro- 
duce?    What  is  the 
product   of  3   times 
2?     What  is  the  pro- 
duct of  3  times  7? 
What  is  the  product 
of  4  times  5  ? 

2.  What  number  does  6  times  4  make?    What  is  the 
product  of  6  times  4  ?   What  is  the  product  of  6  times  7  ? 
What  is  the  product  of  7  times  6  ? 

3.  What  is  the  product  of  4  times  8  ?    Ask  this  ques- 
tion without  using  the  word  product. 


104  MULTIPLICA  TI ON.— EXERCISES  FOR 


4.  What  is  the  product  of  3  and  4  ?     Ask  this  question 
without  using  the  word  product. 

5.  How  many  are  8  times  6  ?    Ask  this  question  and 
use  the  word  product. 

6.  What  is  the  product  of  7  and  3  ? 
What  is  the  product  of  6  and  9  ? 
What  is  the  product  of  8  and  7  ? 
What  is  the  product  of  3  and  9  ? 
What  is  the  product  of  3  and  3  ? 
What  is  the  product  of  8  and  8  ? 

7.  Supply  the  proper  word  in  the  following : 
What  is  the of  6  and  4  ? 

The of  7  and  5  is  what  ? 

9  times  5  gives  what ? 


What  is  the 


of  2  and  9  ? 


Second  Definition  Exercise. 

1.  Here  are  some  curious  onions. 
If  you  plant  a  little  one  like  one 
of  those  in  the  first  row,  it  will 
grow  and  multiply  into  4  or  more 
like  those  in  the  second  row.  If 
you  planted  the  3  in  the  first 
row,  and  each  one  multiplied  so- 
as  to  make  4,  how  many  would 
you  have  ?  How  many  times  as  many  as  you  planted  ? 
3  multiplied  by  4  produces  how  many  ?  What  is  the  pro- 
duct of  3  multiplied  by  4  ? 


PU PILS  READING  SIMPLE    WORDS.    105 

2.  If  I  plant  6  of  these  curious  onions,  and  each  one 
multiplies  into  5,  how  many  times  as  many  shall  I  have 
as  I  planted  ?     6  multiplied  by  5  produces  how  many  ? 

3.  If  I  multiply  5  by  6,  what  is  the  product  ?     When  I 
multiply  6  by  5,  what  is  the  product  ?     When  I  multiply 

5  by  6,  how  many  times  do  I  take  5  ?     G  times  5  are  how 
many  ? 

4.  If  I  multiply  4  by  8,  what  is  the  product  ?     Ask  this 
question  without  using  either  of  the  words  multiply  or 
product. 

5.  If  I 7  by  3,  what  is  the ? 

If  I G  by  9,  what  is  the ? 

The of  5 by  8  is  what  ? 

What  is  the of  7 by  6  ? 

6.  When  you  multiply  8  by  9,  how  many  times  do  you 
takeS?    What  is  the- ? 

7.  What  is  the of  8  and  7  ? 

6 by  4  gives  what  —        -  ? 

What does  4 by  10  give  ? 

8.  Finding  what  the  product  of  two  numbers  is,  is 
called  MULTIPLICATION. 

9.  We  have  now  studied  COUNTING,  ADDITION,  SUB- 
TRACTION, and  MULTIPLICATION.     When  I  find  out  that 

6  taken  from  11  leaves  5,  what  is  it  ?     When  I  find  out 
that  5  times  6  is  30,  what  is  it?     When  I  name  all  the 
numbers  in  order  from  one  to  twenty — thus,  one,  two, 
three,  four,  etc. — what  is  it  ?   When  I  find  out  that  7  and 
8  are  15,  what  is  it  ? 


106  MULTIPLICA  TION.— EXERCISES  FOR 


Drill   Exercise.* 

1.  Add  4  and  3  and  6 ;  from  this  sum  subtract  8 ;  mul- 
tiply this  remainder  by  2.    What  is  the  result  ? 

2.  Add  2  and  6  and  3  and  7 ;  from  this  sum  subtract 
9 ;  multiply  the  remainder  by  3.    What  is  the  product  ? 

3.  Add  5  and  7 ;  from  this  sum  subtract  8 ;  to  this  re 
mainder  add  5 ;  from  this  sum  subtract  7 ;  multiply  this 
remainder  by  4 ;  multiply  this  product  by  3 ;  to  this  pro- 
duct add  6.     What  is  the  result  ? 

4.  From  8  subtract  3 ;  from  this  remainder  subtract 
2 ;  to  this  remainder  add  5  and  7 ;  from  this  sum  subtract 
8;  to  this  remainder  add  2;  multiply  this  sum  by  4. 
What  is  the  result  ? 

5.  Begin  with  5,  add  2,  add  6,  subtract  9,  multiply  by 
3,  add  5,  subtract  8,  subtract  6,  multiply  by  7.    What  is 
the  result  ? 

6.  Begin  with  11,  subtract  6,  subtract  2,  multiply  by  8, 
add  5.    What  is  the  result  ? 

7.  Begin  with  6,  multiply  by  2,  subtract  5,  add  3,  sub- 
tract 4,  add  1,  subtract  6,  add  8,  multiply  by  7.     What 
is  the  result? 

8.  Begin  with  5,  add  7,  subtract  3,  subtract  4,  multiply 
by  3,  add  8.     What  is  the  result  ? 

9.  Begin  with  4,  add  9,  subtract  7,  multiply  by  2,  sub- 
tract  1,  subtract   3,  multiply  by  9.     What  is   the  re- 
sult ? 

10.  Begin  with  6,  add  8,  subtract  7,  add  2,  multiply 
by  8.    What  is  the  result  ? 

*  Drill  exercises  of  this  character  must  be  continually  kept  up  as  oral  ex- 
ercises.    See  foot-note  on  page  76. 


PUPILS  READING  SIMPLE    WORDS.    107 

Practical  Exercises. 

1.  John  bought  2  oranges  for  4  cents  each,  and  gave 
the  clerk  10  cents.     How  much  change  did  he  receive  ? 

2.  Mary  bought  3  spools  of  thread  for  6  cents  each, 
and  one  yard  of  calico  for  9  cents.     How  much  did  she 
pay  for  all  ? 

3.  Henry  worked  3  hours  for  5  cents  an  hour,  and  the 
man  for  whom  he  worked  gave  him  a  ball  worth  8  cents, 
and  the  remainder  in  money  ?     How  much  money  did 
Henry  get  ? 

4.  How  many  days  are  there  in  one  week  ?    How  many 
in  6  weeks  ?     How  many  days  in  4  weeks  ? 

5.  John  worked  1  week  (6  days)   and  4  days  more  ? 
How  many  days  did  he  work  in  all  ?      If  he  earned  4 
shillings  a  day,  how  many  shillings  did  he  earn  ?     How 
many  more  days  would  he  have  had  to  work  to  make  2 
weeks  ?     How  much  more  would  he  have  earned  if  he 
had  worked  2  weeks  ? 

6.  Sarah  sews  3  hours  each  day.     How  many  hours  does 
she  sew  in  a  week  (6  days)  ? 

7.  How   many   days   are   there   in   8   weeks?      How 
many  Sundays  in  8  weeks  ?    How  many  work-days  in  8 
weeks  ? 


108 


DIVISION.— EXERCISES   FOR 


DIVISION. 

Purpose.—^  develop  the  idea  of  division  in  its 
2wo  Forms,*  and  the  nature  of  ^Division  as  the  con- 
verse of  Multiplication,  and  to  deduce  the  quotient 
of  any  number  less  ttian  WO,  divided  by  any  num- 
ber less  than  fO,  f?om  the  relation  of  division  to 
Multiplication* 


First  Exercise.f 


1.  How  many  lit- 
tle ducks  are  there 
in  the  picture?  Are 
they  all  together? 
In  how  many 
groups  are  they? 
How  many  in  each 


group 


?     3 


groups, 


with  4  in  each  group,  make  how  many?  How  many  4's  in  12? 

2.  If  you  have  12  little  ducks  and  put  them  in  3  groups, 

with  the  same  number  in  each  group,  how  many  will 

*  There  are  two  essentially  different  logical  processes   called   division: 

1.  Determining  how  many  times  one  number  is  contained  in  another;  and 

2.  Separating  a  number  into  any  required  number  of  equal  parts,  for  the  pur- 
pose of  finding  how  many  there  are  in  one  of  these  parts.    The  former  is  the 
more  comprehensive  view,  although  the  latter  gives  name  to  the  process.    The 
foundation  for  Division  has  been  so  well  laid  in  Multiplication  that  but  little 
more  will  be  needed  here  than  to  familiarize  the  two  forms  of  conception,  and 
give  practice  to  fix  the  division  table  in  mind. 

t  The  teacher  should  carefully  observe  the  character  and  purpose  of  the  in- 
troductory examples  in  each  of  these  exercises  in  Division,  and  give  ample  ex- 
amples of  the  same  kind,  as  class  exercises,  illustrating  with  the  counters  and 
other  objects.  But  be  sure  and  stick  to  the  point  of  the  particular  exercise. 
Such  questions  as  "  How  many  2's  make  4  ?  "  u  How  many  3's  make  15  ?  "  etc., 
are  of  great  service  in  leading  the  pupil  to  comprehend  the  nature  of  division, 
and  its  relation  to  multiplication. 


PUPILS  READING   SIMPLE    WORDS.    109 

there  be  in  each  group  ?    12  divided  into  3  equal  parts 
makes  how  many  in  each  part  ? 

3.  How  many  a's  are  there  in  the  next  line  ? 

a    a    a    a    a    a 

If  you  divide  these  6  a's  into  groups  with  3  in  a  group, 
how  many  groups  will  there  be  ?  |  a  a  a  a  a  a  . 
How  many  3's  in  6  ?  If  you  divide  6  a's  into  2  equal 
groups,  how  many  will  there  be  in  each  group  ?  6  divided 
by  2  are  how  many  ? 

4.  3  times  what  number  makes  12  ?    How  many  times 
does  4  go  in  12  ?    4  times  what  number  makes  12  ?  How 
many  times  does  3  go  in  12  ?     12  divided  by  4  are  how 
many  ?    Why  ?*    12  divided  by  3  are  how  many  ?    Why  ? 

5.  2  times  what  number  make  6  ?     How  many  are  6 
divided  by  3  ?    Why  ?    3  times  what  number  are  6  ?    6 
divided  by  2  are  how  many  ? 

(NOTE. — Teacher,  explain  that  -*-  means  "  divided  by.") 

6.  Copy,  fill  out,  and  learn  the  following : 


2- 

-2  = 

3- 

-3  = 

8- 

-2  = 

4- 

— 

4- 

-2  = 

6- 

-3  = 

9- 

-3  = 

30- 

-3  = 

6- 

-2  = 

9- 

-3  = 

10- 

-2  = 

14- 

-2  = 

8- 

-2  — 

12- 

-3  = 

6- 

—  O  :=: 

16- 

9  

10- 

-2= 

15- 

-3  = 

6- 

-2  = 

21- 

-3  = 

12- 

<2  

18- 

-3  = 

12- 

-3  = 

2- 

n 

—  A  — 

14- 

-2  = 

21- 

-3  = 

12- 

-2  = 

3- 

-3  = 

16- 

—  2m: 

24- 

-3  = 

15- 

—  o  = 

27- 

-3- 

18- 

-2  = 

27- 

-3  = 

20- 

-2  = 

18- 

o 

—  A  — 

20- 

-2= 

30- 

—3=^ 

18- 

-3  = 

24- 

-3  = 

*  The  point  of  this  question  is  that  the  pupil  may  learn  to  deduce  Division 
from  Multiplication.    Ans.  Because  3  times  4  are  12. 


110 


DIVISION.— EXERCISES  FOR 


Second  Exercise. 

1.  How  many  fingers, 
including  thumbs,  have 
two  boys  ?     How  many 
5's  in  20?    If  you  di- 
vide   20   into    5    equal 
parts,    how    many  will 
there  be  in  each  part  ? 

2.  20-^5=: how  many? 

3.  20H-4:=  how  many? 

4.  How  many  legs  have  6  cats  ?    How  many  4's  in  24  ? 
24-=-4=  how  many  ?    Why  ? 

5.  John  has  28  cents ;  how  many  lemons  can  he  buy  at 
4  cents  each  ?    How  many  4's  in  28  ?    28  -7-  4  =  how 
many  ?    Why  ? 

6.  Mary  has  15  pansies,  and  she  wishes  to  make  5  bou- 
quets and  put  the  same  number  of  pansies  in  each.    How 
many  can  she  put  in  each  bouquet  ?    If  you  divide  15 
things  into  5  equal  groups,  how  many  will  there  be  in 
each  group  ?     15 — 5=  how  many  ? 

7.  Copy,  fill  out  and  learn  the  following: 


4- 

-4= 

5- 

-5  = 

12- 

-4= 

4- 

-4= 

8- 

-4= 

10- 

-5  = 

15- 

-5  = 

5- 

-5  = 

12- 

-4= 

15- 

-5  = 

16- 

-4= 

10- 

-5  = 

16- 

-4== 

20- 

-5= 

28- 

-4= 

35- 

-5  = 

20- 

-4= 

25- 

-5  = 

25- 

-5  = 

32- 

-4= 

24- 

-4— 

30- 

-5  = 

30- 

-5  = 

40- 

-5  = 

28- 

-4=r 

35- 

-5  = 

36- 

-4= 

40- 

-4= 

32- 

-4= 

40- 

-5  = 

20- 

-4= 

45- 

-5  = 

36- 

-4= 

45- 

-5= 

20- 

-5  = 

24- 

-4— 

40- 

-4= 

50- 

-5  = 

8- 

-4= 

50- 

-5  = 

PUPILS  READING   SIMPLE    WORDS.     \\\ 


Third  Exercise.* 

1.  This  large  basket  con- 
tains 42  eggs.  How  many 
times  can  the  little  girl  till 
her  small  basket  from  it,  if 
her  small  basket  holds  6 
eggs  ?  How  many  times 
can  she  fill  her  small  basket 
if  it  holds  7  eggs?  How 
many  6's  in  42  ?  How  many 
times  6  make  42  ?  42-^-6 
are  how  many  ?  Why  ?  How  many  7's  in  42  ? 


How 


many  times  7  make  42  ?  42^7  make  how  many  ?  Why  ? 

2.  Make  30  O's  on  your  slate,  thns  : 

000000000000000000000000000000 

Then  rub  out  6  O's.  Then  rub  out  6  more.  Then  an- 
other 6.  How  many  times  can  you  rub  out  6  O's  ?  How 
many  6's  in  30  ?  How  many  times  6  make  30  ?  30 -r- 6 
are  how  many  ?  Why  ? 

3.  If  John  has  45  cents  and  spends  7  cents  each  day, 
how  many  days   before  all  his  money  will  be  spent  ? 
45  -=-7= how  many  ?     Why? 

4.  If  Henry  has  56  cents,  how  many  oranges  can  he 
buy  at  7  cents  each?     5  6 -f- 7= how  many  ?     Why  ? 


*  The  purpose  in  this  exercise  is  to  show  how  we  may  find  how  many  times 
one  number  is  contained  in  another  by  taking  the  former  from  the  latter  as 
many  times  as  possible  ;  i.  e.,  by  subtraction.  See  note  at  the  bottom  of  page 
108.  That  process  may  be  made  serviceable  for  this  purpose. 


DIVISION.— EXERCISE  S   FOR 


Copy,  fill  out,  and  learn  the  following  : 


6- 

-6  = 

7- 

-7  = 

36- 

-6  = 

6- 

-6 

12- 

-6  = 

14- 

-  7  — 

42- 

ty  

7- 

-7 

18- 

-6r= 

21- 

_  7  — 

42- 

-6  = 

14- 

-7 

24- 

-6  = 

28- 

_  7  — 

30- 

-6  = 

18- 

-6 

30- 

-6  = 

35- 

_  7  — 

35- 

_  7  — 

21- 

-7 

36- 

-6  = 

42- 

-7  = 

49- 

-7  = 

54- 

-6 

42- 

-6  — 

49- 

_  n  

24- 

-6  = 

56- 

-7 

48- 

-6  = 

56- 

ry  

12- 

-6  = 

48- 

-6 

54- 

-6  = 

63- 

-  7  = 

70- 

w  

63- 

-7 

60- 

-6  = 

70- 

-7  = 

60- 

-6  = 

28- 

-7 

Fourth  Exercise. 

1.  Make  18  a's  on  your  slate  thus: 
aaaaaaaaaaaaaaaaaa 

Then  mark  them  off  into  groups  of  9  each.  How  many 
such  groups  will  you  have  ?  How  many  9's  in  18  ?  How 
many  times  9  are  18  ?  18 -=-9=  how  many  ? 

2.  Make  36  a's  on  your  slate  thus : 
aaaaaaaaaaaaaaaaaa 
aaaaaaaaaaaaaaaaaa 

Then  make  9  large  circles 
thus: 

Then  rub  out  one  a  and 
put  it  in  one  of  the  circles. 
Then  rub  out  another  a  and 
put  it  in  another  circle.  Then 
another  and  another,  till  you 
have  one  a  in  each  circle. 
Then  go  round  again  and 


P  UPILS  READING   SIMPLE    WORDS.     H3 

put  another  a  in  each  of  the  circles,  till  you  have  2  a's  in 
each  circle.  Then  go  round  again,  putting  another  a  in 
each  circle,  till  all  the  30  a's  are  used  up.  How  many  a's 
will  there  be  in  each  circle  ?  If  you  divide  36  into  9 
equal  groups,  how  many  are  there  in  each  group  ? 
36  -=-  9  =  how  many  ?  Why  ? 


r» 

o. 


Copy,  fill  out,  and  learn  the  following : 


8- 

-8  = 

9- 

-9  = 

72- 

-9  = 

27- 

-9 

16- 

-8  = 

18- 

-9  = 

72- 

—  8^^ 

32- 

-8 

24- 

-8  = 

27- 

-9  = 

8- 

-$  = 

36- 

-9 

32- 

-8  = 

36- 

-9  = 

9- 

-9  = 

40- 

-8 

40- 

-8  = 

45- 

-9  = 

80- 

-8  = 

45- 

-9 

48- 

-8= 

54- 

-9  = 

90- 

-9  = 

56- 

-8 

56- 

-8= 

63- 

-9  = 

16- 

-8  = 

63- 

-9 

64- 

-8  = 

72- 

-9  = 

18- 

-9  = 

64- 

-8 

72- 

-8  = 

81- 

-9  = 

24- 

-8  = 

81- 

-9 

80- 

—8^= 

90- 

-9  = 

48- 

-8= 

54- 

-9 

Fifth  Exercise. 

1.  How  many  10's  are  there  in  20  ?  How  many  in  30  ? 
In  40  ? 

2.  40-r-10=  how  many  ?    30-7-10=  how  many  ? 

3.  How  many  Ts  in  6  ?     6 -7-1=  how  many?     How 
many  Ts  in  7  ?    7-r-l=  how  many  ? 

4.  Mary  has  80  needles  in  8  papers,  with  the  same 
number  in  each  paper.     How  many  needles  in  each 
paper  ? 


114 


DIVISION.— EXERCISES   FOR 


5.  If  Mary  puts  her  80  needles  up  in  papers  of  10  nee- 
dles each,  how  many  papers  will  she  have?     80-^-8  = 
how  many  ?     S0-r-10  =  how  many  ? 

6.  John  has  60  cents  in  his  bank.    If  he  takes  out  10 
cents  each  day,  how  many  days  before  his  money  will  be 
gone  ?    How  many  times  can  you  take  10  out  of  60  ? 
60-f-10  =  how  many  ? 

I  Copy,  fill  out,  and  learn  the  following : 


7. 


10- 

-10  = 

1- 

-1  = 

50- 

-10  = 

3- 

-  1 

20- 

-10  = 

2- 

-1  — 

8- 

—    1  =: 

2- 

-  1 

30- 

-10  = 

3- 

-1  = 

30- 

-10  = 

60- 

-10 

40- 

-10  = 

4- 

-1  = 

70- 

-10  = 

80- 

-10 

50- 

-10  = 

5- 

—  1^= 

7- 

-  1= 

5- 

-  1 

60- 

-10  = 

6- 

-1  = 

4- 

-  1= 

90- 

-10 

70- 

-10  = 

7- 

—  1  = 

10- 

-10  = 

6- 

-  1 

80- 

-10  = 

8- 

—  1  = 

1- 

_  1  — 

9- 

-  1 

90- 

-10  = 

9- 

-1  = 

20- 

-10  = 

100- 

-10 

100- 

-10  = 

10- 

-1  = 

40- 

-10  = 

10- 

-  1 

Sixth  Exercise. 

1.  Here  is  a  beautiful  pansy. 
How  many  blossoms  are  there  on 
it?  If  you  make  2  bouquets 
and  put  3  of  these  pansies  in 
each  of  them,  how  many  pansies 
will  remain  ?  How  many  o's  in 
8,  and  how  many  over  ? 


PUPILS  READING  SIMPLE    WORDS.    115 

2.  John  had  15  cents  and  gave  4  cents  apiece  for  3 
oranges.   How  many  cents  did  he  have  remaining  ?  How 
many  times  can  you  take  4  from  15  ?     How  many  will 
remain  after  you  have  taken  4  from  15  as  many  times  as 
you  can? 

3.  Are  there  4  2's  in  7  ?    How  many  2's  are  there  in  7  ? 
Is  there  any  remainder  after  you  have  taken  3  2's  from  7  ? 
What  is  it  ? 

4.  How  many  are  5  times  7  ?     6  times  7  ?    How  many 
7's  are  there  in  38,  and  how  many  over  ?    How  many  7's 
in  40,  and  how  many  over  ?    How  many  7's  in  37,  and 
how  many  remaining  ? 

5.  If  you  divide  12  into  as  many  5's  as  you  can,  how 
many  5's  will  you  have,  and  how  many  remaining  ?     If 
you  divide  23  into  as  many  6's  as  you  can,  what  will  the 
remainder  be  ?    3x6=  how  many  ?    4x6=  how  many  ? 
Are  there  4  6's  in  23  ? 

6.  Say  the  "3  times"  of  the  Multiplication  Table.   Are 
there  2  3's  in  17  ?     Are  there  3  3's  in  17  ?     Are  there  4  ? 
Are  there  5  ?    Are  there  6  ?    How  many  3's  are  there  in 
17,  and  how  many  over  ? 

7.  Say  the  "  6  times  "  of  the  Multiplication  Table.   Are 
there  3  6's  in  27  ?    Are  there  4  ?    Are  there  5  ?    If  you 
divide  27  into  as  many  6's  as  you  can,  how  many  6's  will 
you  have,  and  what  remainder  ? 

8.  Say  the  "  8  times  "  of  the  Multiplication  Table.  Are 
there  3  8's  in  47  ?    Are  there  4  ?    Are  there  5  ?    Are 
there  6  ?      How  many  times  is  8  contained  in  47,  and 
how  many  remain  ? 


116  DIVISION.— EXERCISES  FOR 

Seventh  Exercise. 

1.  Say  the  "4  times"  of  the  Multiplication  Table.   Are 
there  3  4's  in  27  ?    Are  there  5  4's  in  27  ?    Are  there  6  ? 
Are  there  7  ?     How  many  4's  in  27,  and  what  is  the  re- 
mainder?   27-^4  are  how  many,  and  what  is  the  remain- 
der ? 

2.  John  had  35  cents  and  bought  8  lead-pencils,  at  4 
cents  each.    How  much  money  had  he  left  ?     How  many 
4's  in  35,  and  how  many  remain  ? 

3.  Copy,  and  fill  out  the  following : 


jLrt— 
00 

\  

q  }~\f\ 

X  V_llL(lill'tVI  • 

-  TpmainrlpT* 

/c/c 
18 

"±  - 
1  

—  dlin. 

infl 

-  VPTTI  a  i  n  rl  PI* 

-LO 

q*y 

K 

nv»  /i 

VAITI  Q  m  n  PI* 

o  <  — 
4.0 

<J  

a 

dllU. 
o  IT  n 

~   1  CillcllilLlCl  • 

_  VAmQTnnPT* 

ttu  — 

K1 

7 

O  Tl  (  1 

TP  vn  ft  i  n  rl  PT* 

tjL  — 

78- 

fi7 

i  — 
-9=  — 

ttllU.  - 

—  and  — 

n  n  n 

~    lCllJu.lll>-tCJ.. 

—  remainder. 

VPTYI  fi  in  rl  PT 

D  1  — 
QA 

— 

Q 

on  rl 

1  C  LllCllllVACi  . 

_  vom  m  n  n  PT 

OU            €/  - 

Drill  Exercise.* 

1.  Add  2,  3,  4,  subtract  6,  multiply  by  7,  divide  by  3, 
subtract  5,  add  7,  divide  by  3,  multiply  by  8,  divide  by  6, 
add  9,  add  7,  divide  by  5,  divide  by  2,  add  8,  3,  9,  2,  4, 
divide  by  7.  What  is  the  result  ? 

*  We  repeat  that  this  character  of  exercise,  either  wholly  oral  or  by  means 
of  blackboard,  arithmetical  roll,  or  lattice,  must  be  constantly  kept  up.  No  day 
should  pass  in  a  primary  school  without  more  or  less  of  this  drill  in  combining 
numbers. 


PUPILS  READING  SIMPLE    WORDS.  117 

2.  Add  5  to  7,  subtract  8,  multiply  by  3,  add  9,  divide 
by  7,  add  8,  subtract  9,  add  6,  multiply  by  7,  add  8,  divide 
by  8.     What  is  the  result  ? 

3.  From  13  subtract  8,  multiply  by  4,  add  6,  add  4,  add 
2,  divide  by  4,  divide  by  2,  multiply  by  7,  add  8,  divide 
by  9.     What  is  the  result  ? 

4.  Divide  54  by  6,  divide  by  3,  multiply  by  9,  add  8, 
add  10,  divide  by  9,  multiply  by  6,  add  5,  divide  by  7, 
multiply  by  2,  multiply  by  7,  add  2,  divide  by  8,  multiply 
by  6,  add  9,  divide  by  7,  divide  by  9,  subtract  1.     What 
is  the  result  ? 

5.  Divide  27  by  9,  multiply  by  3,  add  5,  add  4,  divide 
by  6,  multiply  by  8,  add  8,  add  4,  divide  by  6,  multiply 
by  7,  add  7,  divide  by  1,  multiply  by  9,  add  1,  divide  by  8. 
What  is  the  result  ? 

6.  Divide  56  by  7,  multiply  by  6,  add  6,  divide  by  9, 
multiply  by  7,  add  7,  3,  6,  4,  1,  divide  by  9,  multiply  by 

8,  add  10,  10,  5,  divide  by  9.     What  is  the  result  ? 

7.  From  15  subtract  9,  add  2,  multiply  by  8,  add  6, 
divide  by  10,  multiply  by  9,  add  1,  divide  by  8,  subtract 
1,  multiply  by  7,  add  7,  divide  by  9.    What  is  the  re- 
sult? 

8.  Divide  56  by  7,  divide  by  2,  multiply  by  8,  add  3, 
divide  by  7,  add  4,  multiply  by  6,  add  9,  divide  by  7. 
What  is  the  result  ? 

9.  From  13  subtract  8,  multiply  by  6,  add  6,  divide  by 

9,  multiply  by  8,  add  4,  divide  by  6,  subtract  6,  multiply 
by  3.     What  is  the  result  ? 

6 


SECTION    III. 


FRACTIONS, 


Purpose 


teach  the  signification  of  the  frac- 
tions i,  f,  i,  |,  f,  i,  f,  f,  f,  i,  f,  £/c.,  /<9  tenths  inclusive, 
and  how  to  get  any  such  fractional-  part  of  a  num- 
ber* 

First  Exercise. 

1.  If  you  cut  an   apple  into   2 
parts  of  just  the  same  size,  what  do 
you  call  one  of  the  parts?     If  you 
cut  an  apple  into  2  parts  so  that 
one  of  the  parts  shall  be  larger  than 
the  other,  will  either  of  the  parts  be 
a  half  an  apple?     In  the  lower  pic- 
ture, is  the  part  of  the  apple  on  the 
right  more  than  half  the  apple,  or 
less  than  half? 

2.  When  you  divide  anything  into  halves,  how  many 
parts  do  you  make  of  it  ?     How  many  halves  in  the  whole 
of  anything  ?     Which  half  of  an  orange  is  the  larger  ? 


FRACTIONS. 


119 


3.  Into  how  many  parts  is  this 
apple  divided  ?    Are  the  parts 
of  equal  size  ?    What  is  one  of 
the  3  equal  parts  of  anything 
called?    A  us.  One  Third. 

4.  Into  how  many  parts  is  this 
apple  divided?    Is  this  apple 
divided  into  thirds  ?   Why  not  ? 

5.  How  many  thirds  are  there 
in    the    whole    of    anything  ? 
Which  third   of  an   orange  is 
the  largest  ?    If  you  divide  an 

apple  into  thirds  and  give  away  two  of  them,  how  many 
will  you  have  left  ?  What  part  of  the  apple  will  you  have 
left  ?  What  part  will  you  have  given  away  ? 

6.  Here  are  10  cherries  on  a 
plate.   If  you  divide  them  equally 
between  two  girls,  what  part  of 
the  cherries  will  each  girl  have  ? 
How  many  will  each  girl  have  ? 

One-half  of  10  is  how  many  ?  10-^-2  =  how  many  ?  By 
what  must  you  divide  a  number  to  get  one-half  of  it? 

7.  Here  are  12  nuts.    If  you 
divide  them  equally  among  3 
boys,  what  part  of  the  nuts  will 
each  boy  receive  ?     How  many 
nuts  will  each  boy  have  ?   12-^ 


3  =  how  many  ?    By  what  must  we  divide  a  number  to 
get  one-third  of  it  ? 


120 


SIGNIFICA  TION    OF 


8.  One-half  is  written 
One-third  is  written 
Two-thirds  is  written  f . 

What  does  ^  mean  ?    What  does  J  mean  ?    What  does 
mean  ? 

9.  Copy  and  fill  out  the  following: 

of  8  = 
of  9  = 
of  6  = 
of  6  = 
of  10  = 
i  of  4= 


of  18= 

|  of    6  = 

of  18  = 

|  of  12  = 

of  16  = 

f  of    9  = 

of  21  = 

|  of  21  = 

of    2  = 

|  of  30  = 

of    3  = 

f  of  27  = 

|  of    3  = 

f  of  15  = 
|  of  18  = 


of 
of 
of 


-J  

1— 
1= 


Second  Exercise. 

1.  Into  how  many  equal  parts 
is  this  apple  divided  ?    If  any- 
thing is  divided  into  four  equal 
parts,  what  are  the  parts  called  ? 
Ans.     Fourths.        How    many 
fourths   in   the  whole   of  any- 
thing ? 

2.  If  John   has  a  cake  and  gives  one-fourth  of  it  to 
Henry,  one-fourth  to  Mary,  and  one-fourth  to  Jane,  how 
much  has  he  left  ? 

3.  If  you  divide  12  flowers  equally  among   four  boys, 
what  part  of  them  all  does  one  boy  get?     How  many 
flowers   does   one  boy   get?      One-fourth   of  12   is  how 
many  ?     12  -+-  4  =  how  many  ?     By  what  do  you  divide 
to  get  one-fourth  of  any  number  ? 


FRACTIONS. 


121 


4.  Into  how  many  parts   is 
this  apple  divided?     Are  the 
parts  equal  ?     If  anything  is 
divided  into  5  equal  parts,  what 
is  any  one  of  the  parts  called  ? 
Ans.,  Fifths.    How  many  fifths 
in  the  whole  of  anything? 

5.  If  James  gives  away  three- 
fifths  of  his  melon,  how  many  fifths  will  he  have  left  ? 
Into  how  many  parts  must  a  melon  be  divided  so  that  the 
parts  shall  be  fifths  ?   How  many  fifths  in  a  whole  melon  ? 

6.  Henry  has  15  nuts,  and  divides  them  equally  be- 
tween 5  boys.     What  part  of  ah1  the  nuts  does  one  boy 
receive  ?     If  2  of  the  boys  put  their  shares  together, 
what  part  of  all  the  nuts  will  they  make  ?     One-fifth  and 
one-fifth  make  how  many  fifths  ? 

7.  How  many  nuts  are  one-fifth  of  20  nuts  ?     20-f-5  = 
how  many  ? 

8.  How  many  are  two-fifths  of  20  nuts  ?     Three-fifths  ? 
By  what  do  you  divide  to  get  one-fifth  of  any  number  ? 

9.  One-fourth  is  written  J.    One-fifth  is  written  ^.   Two- 
fourths  is  written  f .     Two-fifths  is  written  f .     The  num- 
ber above  the  short  line  shows  how  many  fourths  or  fifths 
are  meant. 

10.  What  does  f  mean  ?   What  does  f  mean  ?   What 

11.  Copy,  and  fill  out  the  following : 


I  of  12  = 

f  of  20  = 

|  of  35  = 

|  of  30 

\  of  10  = 

f  of  12  = 

f  of  45  = 

|  of  30 

-1  of  30  = 

J  of  32  = 

f  of  25  = 

f  of  30 

J-  of  40  = 

f  of  10  = 

|  of  10  = 

|  of  30 

I  of  32  = 

\  of  35  = 

f  of  15  = 

i  of    8 

SIGNIFICA  TION   OF 


Third  Exercise. 

1.  Into  how  many  parts  is 
this  apple  divided  ?    Are  the 
parts  equal  ?     One  of  the  6 
equal  parts  into  which   the 
whole  of  anything  may  be  di- 
vided is  called  a  sixth.    How 
many  sixths  in  the  whole  of 
anything  ? 

2.  One   of  the   six   equal 

parts  of  the  apple  is  called  what  ?     Then  2  of  the  six 
equal  parts  would  be  what  ?     Three  ?    Four  ?     Five  ? 

3.  You  see  that  one-fourth  of  the  whole  of  anything  is 
one  of  the  4  equal  parts  of  it.     One-fifth  is  one  of  5  equal 
parts.     One-sixth  is  one  of  6  equal  parts.     What,  then,  is 
one-seventh  of  the  whole  of  anything  ?      One-eighth  ? 
One-ninth  ?     One-tenth  ? 

4.  If  an  apple  is  divided  into  7  equal  parts,  what  is  one 
of  the  parts  called  ?     What  are  2  of  the  7  equal  parts 
called?    Three?    Four?    Five? 

Six  ?     Seven  ? 

5.  Here  is  the  whole  of  an 
apple  which  has  been  divided 
into  8  equal  pieces.   Part  of  the 
pieces  are  on  one  plate,  and  part 
are  on  the  other.     How  much 
of  the   apple  is  on  the  upper 
plate  ?      How    much    on    the 
lower  ? 


FRA  CT  IONS. 


123 


6.  If  you  have  36  nuts  and  divide  them  equally  among 
9  boys,  what  part  of  the  whole  does  one  boy  get  ?     How 
many  nuts  does  one  boy  get  ?     How  many  do  2  boys  get  ? 
Three  boys  ?     Three-ninths  of  36  are  how  many  ?     How 
do  you  get  one-ninth  of  any  number? 

7.  What  does  ^  mean  ?     \  ?     \  ? 

8.  What  does  |  mean  ? 


f  ? 


f  ? 


2.? 
3   ' 


4? 
I? 


JL? 
8  ' 


4? 
8  ' 


V 


10* 
V      2.  V 


__ 
10 


Fourth  Exercise.* 


1.  Copy,  and  fill  out  the  following: 


f  of  12  = 
f  of  10  = 
f  of  14= 
f  of  18  = 


}  of  12  = 
|  of  16  = 


__3__  Of  An  — 

1  0     U1 

I  of  30  = 
of  35  = 


f  of  42  = 


f  of  50= 
of  21  = 


f  of  54= 


of  63  = 

of  81  = 

of  56  = 
|  of  40= 

of  24= 

of  32  = 
f  of  72= 

2.  Write  in  figures  on  your  slate,  one-half,  one-third, 
two-thirds,  three-fourths,  five-eighths,  three-eighths,  5 
sixths,  4  sevenths,  eight-ninths,  5-nmths,  three-tenths, 
7-tenths,  4-ninths,  2-ninths,  2-fifths,  two-sevenths. 


f  of  56  = 
f  of  81  = 
f  of  72  = 
of  90  = 
of  90  = 
of  80  = 


of  72  = 


of  64= 

of  72  = 
of  70= 


*  Exercises  of  thie  character  should  be  assigned  by  writing  them  on  the 
blackboard  until  they  can  be  performed  with  the  utmost  ease.  It  affords  an 
excellent  drill  in  division  and  multiplication. 


124 


SIGNIFICATION    OF 


Fifth   Exercise.* 


1.  Here  are  how  many 
whole  apples  ?  How  many 
half  apples?  How  many 
in  all?  We  write  Three 
and  a  half  thus  : 


2.  How  many  whole 
apples  are  there  in  this 
picture  ?  How  many 
pieces?  "What  are  the 
pieces  —  halves,  thirds,  or 
quarters  ?  The  number 
of  apples  in  this  picture  is  written  thus  :  2-f. 
tell  what  2-1  means  ? 


Can  you 


3.  Eead  the  following:  1|,  2£,  4^,  5f,  3|,  6f,  lOf 

4.  There  are  5  apples  on 
the  plate.   If  John  takes  half 
and  Henry  half,  how  many 
will  each  have  ?     Write  the 
number. 

5.  If  7  apples  are  divided  equally  among  3  boys,  how 
many  will  each  boy  have?     If  each  boy  takes  3,  how 
many  will  remain  ?      What  must   they  do  with   that  ? 
What  does  3J-  mean  ? 

6.  If  15  apples  are  to  be  divided  equally  between  4  boys, 


*    The  purpose  of  this  exercise  is  to  teach  the  meaning  of  such  mixed  num- 
bers as  4-J,  31, 10|,  If,  etc.,  and  how  to  read  them. 


FRACTIONS.  125 

how  many  will  each  boy  have  ?  If  each  boy  takes  3 
apples,  how  many  will  be  left  ?  If  now  these  3  apples 
which  are  left  be  divided  into  fourths,,  how  many  fourths 
will  they  make  ?  Now  if  these  12  pieces  are  divided 
equally  among  the  4  boys,  how  many  of  them  will  each 
boy  get  ?  How  many  whole  apples  will  each  boy  have  ? 
How  many  fourths  ?  AY  hat  is  4J  ? 

7.  If  14  apples  are  divided  equally  among  3  boys,  how 
many  whole  apples  and  how  many  thirds  will  each  boy 
get?     14-^-3=  how  many,  and  how  many  over? 

8.  If  30  apples  are  divided  equally  among  7  boys,  how 
many  whole  apples  will  each  boy  have  ?     30  -f-  7  =  how 
many,  and  what  remainder  ?   After  each  boy  has  received 
his  4  whole  apples,  how  many  apples  are  there  left  ?     In 
order  to  divide  an  apple  equally  among  7  boys,  into  what 
parts  must  it  be  divided  ?     If  each  of  2  apples  is  divided 
into  7  parts,  how  many  parts  are  there  ?     How  many 
whole  apples  and  how  many  sevenths  will  each  boy  have  ? 

9.  If  35  oranges  are  divided  equally  among  8  boys,  how 
many  will  each  boy  have  ?     AYill  he  have  4f  or  4-f-  ? 


Practical   Exercises. 

1.  John  and  James  bought  a  melon  worth  8  cents, 
which  they  are  to  share  equally.     How  much  ought  each 
to  pay  ?    AVhat  part  of  the  price  must  John  pay  ?    -J  of  8 
is  how  much  ?     How  do  you  get  \  of  any  number  ? 

2.  John,  James,  and  Henry  bought  a  pie  worth  1 2  cents, 
which  they  are  to  share  equally.     How  much  must  each 
pay  ?     AVhat  part  of  the  price  must  Henry  pay  ?     How 

6* 


126       SIGNIFICATION    OF   FRACTIONS. 

do  you  get  \  of  any  number  ?  How  much  must  John 
and  James  together  pay  ?  What  part  of  the  pie  do  John 
and  James  together  own  ?  -f  of  12  =  how  much  ? 

3.  Mary  and  Jane  bought  a  doll  for  63  cents.     Mary 
paid  |  of  the  price.   What  part  of  the  price  did  Jane  pay  ? 
|  of  63=  how  much?     f  of  63  =  how  much?     How 
many  cents  did  Mary  pay  ?     How  many  did  Jane  pay  ? 

4.  Henry  started  to  market  with  56  eggs,  but  broke  \ 
of  them.     How  many  did  he  break  ?    What  part  of  the 
eggs  remained   unbroken  ?    How  many  eggs  were  un- 
broken ? 

5.  Mary's  hen  had  a  brood  of  12  chickens,  but  a  hawk 
caught  f  of  them.     How  many  had  she  left  ?     If  f  were 
caught,  how  many  thirds  remained  ?     ^   of  12  =  how 
many  ? 

6.  John's  suit — coat,  vest,  and  pantaloons — cost  9  dol- 
lars.    The  coat  and  vest  cost  f  of  the  whole.     What  part 
of  the  whole  did  the  pantaloons  cost  ?    How  many  dollars 
did  the  pantaloons  cost  ? 

7.  Mary  has  f  of  an  apple,  Jane  f ,  and  Henry  the  rest. 
How  much  of  the  apple  has  Henry  ? 

8.  If  one  cord  of  wood  costs  6  dollars,  how  much  will 
\  of  a  cord  cost  ?     \  of  a  cord  ?    f  of  a  cord  ? 

9.  I  had  21  dollars,  and  spent  -f  of  it  for  a  pair  of  boots, 
and  -f  for  a  coat.     What  part  of  my  money  had  I  left  ? 
How  many  dollars  ? 

10.  Our  cistern  was  entirely  dry  on  Saturday.     But  it 
rained  on  Sunday,  and  filled  it  \  full.     On  Monday  it 
rained  again,  and  the  cistern  filled  up  so  that  it  was 
full.     How  much  ran  in  on  Monday  ? 


SECTION    IV. 


DENOMINATE  NUMBERS. 


Purpose.— To  teacfi  a  fen'  of  the  more  common 
denominations  of  measure,  weight,  and  money,  so 
that  the  pupil  shall  hare  a  clear  conception  of  each, 
and  a  knowledge  of  their  mutual  relations. 


First  Exercise. 
UNITED   STATES  MONEY. 

1.  What  is  this  a  picture  of?    What 
is  such  a  piece  of  money  made  of? 

Answer. — This  is  a  picture  of  our  common  cent, 
which  is  made  of  bronze.  Bronze  is  copper  and 
tin  melted  together. 

2.  What  is  this  a  picture  of?     What 
is  such  a  piece  of  money  made  of?     How 
many  cents  is  such  a  piece  worth  ? 

3.  How   many   cents  is  a  half  dime  ? 
How   many   cents  in  2  dimes?      In 
dimes  ? 


128  DENOM.  NUMBERS.— EXERCISES  FOR 


4.  Here  are  two 
pieces   of   money. 
What    are    they  ? 
Which  is  the  most? 
If  they  are   both 

dollars,  why  is  it  that  one  is 

so  much  larger  than  the  other  ? 

Will  the  little  one  buy  just  as 

much  as  the  big  one  ?     How 

many  cents  is  a  dollar  worth  ? 

How  many  dimes  in  100  cents?     100^10— how  many? 

How  many  dimes  make  a  dollar  ? 

5.  What  piece  of  money  is  this? 
What  is  it  made  of?     How  many 
dimes  in   a   dollar?     Then  how 
many  dimes  is  a  half-dollar  worth? 
Five  dimes  are  how  many  cents  ? 
How  many  cents  in  a  half-dol- 
lar ? 

6.  What  are  these  pieces  ? 
Which  is  worth  the   most? 
Why  is  one  so  much  larger 
than  the  other  ?   How  many 
dimes  in  a  half-dollar  ?  Then 

how  many  5-cent  nickels  does  it  take  to  make  half  a 
dollar  ?     How  many  half-dimes  make  a  half-dollar  ? 

7.  Here  is  a  quarter  of  a  dollar.   How 
many  quarters  of  a  dollar  does  it  take 
to  make  a  half-dollar  ?     What  part  of 
a  half-dollar  is  a  quarter-dollar  ?   How 
many  5-cent  nickels  does  it  take  for 
half  a  dollar?    Then  how  many  for 


PUPILS  READING   SIMPLE    WORDS.     129 

a  quarter  of  a  dollar?  How  many  cents  in  a  half-dime  ? 
How  many  half-dimes  in  a  quarter-dollar  ?  How  many 
cents  in  a  quarter-dollar  ? 

8.  What  is  a  ten-cent  piece  called  ?     What  is  a  50-cent 
piece  called  ?     What  is  a  25-ceiit  piece  called  ? 

9.  Learn  this 

TABLE  OF  UNITED   STATES  MONEY. 

10  cents  =  I  dime. 
10  dimes  =  1  dollar. 
25  cents   =  J  dollar. 
50  cents  =  J  dollar. 

9.  John  bought  an  arithmetic  for  half  a  dollar,  a  slate 
for  2  dimes,  a  sponge  for  half  a  dime,  and  a  pencil  for  a 
cent.    How  much  did  all  cost  him  ? 

10.  The  character  $  signifies  dollars,  and  is  written  be- 
fore the  figure  or  figures  telling  how  many.     Thus,  $8, 
means  8  dollars.     $23  means  23  dollars,  etc. 

11.  Figures  representing  cents  are  written  right  after 
those  representing  dollars,  with  a  period,  called  a  Decimal 
Point,  between   the   dollars   and   cents.      Thus,   $12,15 
means  12  dollars  and  15  cents.     $58.37  means  58  dollars 
and  37  cents,   c.,  or  ct.,  is  used  as  an  abbreviation  for  cents. 
Thus,  28  c.,  or  28  ct.,  is  28  cents. 

12.  Eead  $62.25;   $5.18;    $7.30;  $19.03.     The  last  is 
19  dollars  and  3  cents,  since  03  is  just  the  same  as  3.   We 
have  to  put  the  0  before  the  3  when  we  write  dollars  and 
cents  together;  otherwise  we  could  not  tell  whether  the 
3  did  not  mean  30  cents.     Thus,  $19.3  would  be  the  same 
as  $19.30. 

13.  Eead  $8.05;  $8.50;  $10.10;  $10.01;  $0.58;  $0.23; 
$100;  $100.05. 


130  SIMPLE    LESSONS   IN 

Second  Exercise.* 

MEASURES  OF  LENGTH.f 

1.  When  we  wish  to  tell  how  long  anything  is,  we  say 
it  is  so  many  inches,  feet,  yards,  rods,  or  miles.  You  will 
need  to  learn  just  how  long  each  of  these  measures  is. 
This  short  line  is  1  inch  long,  and  the  long  one  is  3  inches 
long. 


1  INCH 
I 


3  INCHES 


2.  Get  a  little  stick,  or  a  little  narrow  slip  of  paper,  and 
cut  it  off  just  1  inch  long ;  that  is,  just  as  long  as  the 
short  mark.  Then  make  a  mark  on  your  slate  4  times  as 
long  as  your  inch  measure.  Make  another  5  times  as 
long.  Make  another  6  inches  long.  Another  7  inches 
long. 

*  The  exercises  following  these  tables  are  only  given  as  specimens  of  what 
the  teacher  should  do  in  connection  with  the  memorizing  of  the  tables  by  the 
pupils.  It  is  specially  true  on  this  subject  that  no  book  can  supply  what  the 
pupil  needs.  He  must  learn  to  judge  of  measures  and  weights— i.  e.,  to  have 
some  just  conception  of  magnitudes  and  quantities,  and  to  measure  them  by 
the  proper  apparatus,  as  measuring-rulers,  rods,  cups,  weights,  etc. 

t  No  good  work  can  be  done  in  this  subject  without  a  little  apparatus. 
Thus,  for  length,  a  foot-ruler,  divided  into  inches,  and  a  yard-stick,  divided  on 
one  side  into  feet  and  on  the  other  into  halves,  quarters,  and  eighths,  as  on  the 
dry-goods  merchant's  counter.  These  the  pupils  must  handle  and  apply. 
Practice  in  guessing,  and  then  testing  the  guess,  will  be  entertaining  and  prof- 
itable. The  apparatus  needed  for  other  uses  will  be  specified  in  its  place. 


DENOMINATE    NUMBERS.  131 

3.  Is  this  page  5  inches  wide  ?   Is  it  4  inches  wide  ?    Is 
it  any  more  than  4  inches  wide  ?    How  long  is  this  page  ? 

4.  Get  another  stick  long  enough  so  that  you  can  cut 
off  a  piece  just  12  times  as  long  as  your  inch  measure.* 
A  stick  that  is  12  inches  long  is  just  a  foot  long.     So  we 
say,  12  inches  make  1  foot.     Or  we  write  it,  12  inches  = 
1  foot. 

5.  How  many  inches  long  is  your  desk  ?   Do  you  think 
it  is  a  foot  long  ?    Is  it  a  foot  wide  ? 

6.  Learn  the  following 

TABLE  OF  LINEAR  MEASURES. 

12    indies  =  I  foot. 
3  feet      =  1  yard. 
5|  yards  =  1  rod. 
320    rods     =  1  mile. 

Abbreviations. — in.  stands  for  inch,  or  inches  ;  ft.  for 
foot,  or  feet ;  yd.  for  yard,  or  yards ;  rd.  for  rod,  or  rods ; 
and  mi.  for  mile,  or  miles. 

7.  Do  you  think  the  door  is  a  yard  wide  ?     How  many 
yards  high  do  you  think  it  is  ? 

8.  If  a  door  is  two  yds.  high,  how  many  feet  high  is 
it  ?     How  many  feet  long  is  a  blackboard  that  is  3  yds. 
long  ? 

9.  How  many  yards  make  a  rod  ?     Do  you  think  this 
room  is  a  rod  wide  ?     Is  it  more  than  a  rod  wide  ?     How 
many  rods  long  do  you  think  it  is  ? 


*  The  teacher  should  allow  (require,  if  necessary)  each  pupil  to  have  such 
sticks,  and  measure  with  them. 


132  SIMPLE    LESSONS   IN 

10.  How  many  rods  wide  do  you  think  the  school-yard 
is  ?     If  you  had  a  stick  1  yard  long,  could  you  measure 
and  find  out  how  wide  the  yard  is  ?    How  many  times 
the  length  of  the  yard-stick  does  it  take  to  make  a  rod  ? 

11.  How  many  feet  long  is  a  yard  ?    How  many  feet  is 
a  half  a  yard  ?     How  many  inches  in  a  foot  ?    How  many 
inches  in  one  foot  and  a  half?     How  many  inches  in  half 
a  yard  ? 

12.  This  ruler  is  divided  as  a  yard-stick  is  usually,  only 
it  is  but  3  in.  long  instead  of  3  ft.     What  part  of  the 


whole  length  is  it  from  either  end  to  the  two  dots  ?  What 
part  from  either  end  to  the  one  dot  nearest  that  end  ? 
What  part  is  it  from  the  one  dot  to  the  two  dots  ?  How 
many  fourths  of  a  yard  in  a  half-yard  ? 

13.  Do  you  know  what  other  name  we  give  to  one- 
fourth  of  anything?     We  often  call  it  a  quarter.    How 
many  inches  in  a  half  a  yard  ?     How  many  in  a  quarter 
of  a  yard  ? 

14.  If  there  are  9  in.  in  a  quarter  of  a  yard,  and  4  quar- 
ters in  a  yard,  how  many  inches  are  there  in  a  yard  ? 

15.  How  many  inches  in  a  half  a  foot  ?     How  many  in 
a  quarter  of  a  foot  ? 

16.  How  many  inches  in  !£/£.?     In 


NOTE.—  The  teacher  should  give  the  pupils  as  good  an  idea  of  a  mile  as  pos- 
sible, by  referring  to  distances  with  which  they  are  familiar,  as  to  some  house 
a  mile  off,  a  half-mile  off,  2  miles  off,  etc.  Also  by  the  time  it  takes  them  to 
walk  a  mile,  etc.  Such  questions  as  this  will  help  :  Would  it  tire  you  to  walk 
a  rod  ?  Two  rods  ?  A  mile  ?  Two  miles  ? 


DENOMINATE    NUMBERS. 


133 


Third  Exercise.* 


MEASURES  FOR   LIQUIDS. 


EL  =  311/2I 


1.  If  you  were  to  go  to  the  grocery  to  buy  molasses,  or 
kerosene,  or  vinegar,  how  would  you  tell  the  groceryman 
how  much  you  wanted  ?  Which  is  the  more,  a  pint  or  a 
quart  ?  Which  is  the  more,  a  quart  or  a  gallon  ?  Do  you 
know  about  how  large  a  cup  it  takes  to  hold  a  pint  ?  A 
pint  cup  will  hold  about  twice  as  much  as  a  common  tea- 
cup. 


*  To  teach  this  suhject  properly,  a  gallon  measure,  quart  measure,  and  pint 
measure  are  essential.  Fill  the  quart  measure  from  the  pint,  and  vice  versa. 
Also  the  gallon  from  the  quart,  etc.  Half-gallons  aiid  half-pints  are  useful 
also. 


134  SIMPLE    LESSONS   IN 

2.  Learn  the  following 

TABLE  OF  LIQUID  MEASURES. 

2   pints     —  1  quart. 

4    quarts  =  1  gallon. 

31-J  gallons  =  1  barrel. 

Abbreviations. — pt.  stands  for  pint,  or  pints;  qt.  for 
quart,  or  quarts ;  gal.  for  gallon,  or  gallons ;  and  bbl.  for 
barrel,  or  barrels. 

3.  Do  you  think  a  common  water-pail  holds  a  gallon  ? 
Do  you  think  it  holds  2  gal.  ?    3  gal.  ?    4  gal.  ? 

4.  Do   you   think  that  a  common  drinking  tumbler 
holds  a  quart  ?     Do  you  think  it  holds  a  pint  ?    How 
much  do  you  think  it  holds  ? 

5.  I  have  heard  a  boy  who  was  very  thirsty  say  that  he 
could   drink  a  gallon.     Could  he  ?     Could  he  drink  a 
pint  ?    A  quart  ?* 

6.  If  you  wanted  to  measure  out  a  gallon  of  water  and 
had  nothing  but  a  pint  cup  to  measure  with,  how  many 
cupful s  would  you  have  to  take  ? 

7.  What  part  of  a  quart  is  a  pint  ?    What  part  of  a 
gallon  is  a  quart  ? 

8.  How  many  pints  in  7  qt.  ? 

9.  How  many  quarts  in  10^.  ? 

10.  How  many  quarts  in  10  gal.  ? 

11.  How  many  pints  in  3  gal.  ? 


*  In  such  ways  and  by  allowing  (requiring)  the  pupils  to  use  the  measures, 
eeek  to  give  them  correct  notions  of  these  measures.  Let  them  find  out  hy 
actual  trial  that  2  pints  =  1  quart,  and  that  4  quarts  =  1  gallon. 


DENOMINATE    NUMBERS. 


135 


Fourth  Exercise.* 
MEASURES  FOR  GRAINS,  SEEDS,  ETC. 

1.  Here  are  two  cups,  and 
each  is  called  a  quart  cup. 
Are  they  of  the  same  size? 
Measure  them  and  see  which 
is  the  wider.     Which  is  the 
higher  ?     Well,  the   smaller 

one  is  such  a  quart  cup  as  we  measure  milk,  water,  vine- 
gar, or  any  liquid  in ;  while  the  larger  is  such  a  quart  cup 
as  we  use  to  measure  seeds,  grain,  and  any  dry  substances 
which  we  wish  to  measure  in  this  way.  So  you  see  that 
a  quart  of  wheat  is  more  than  a  quart  of  water.  So  also 
a  pint  of  corn  is  more  than  a  pint  of  milk.  It  takes 
about  7  quarts  of  liquid  measure  to  make  as  much  as  6 
quarts  of  dry  measure ;  f  because  the  quart  cup  by  which 
we  measure  liquids  is  so  much  smaller  than  that  by  which 
we  measure  grain,  seeds,  and  other  dry  substances. 

2.  Learn  the  following 

TABLE   OF   DKY    MEASURES. 

%  pints     =  1  quart 
8  quarts  —  1  peck. 
Specks     =  1  bushel. 


*  For  teaching  the  Dry  Measures,  a  pint  measure,  a  quart  measure,  a  four- 
quart  measure,  peck  measure,  and  half-bushel  measure  are  important.  A 
bushel  basket  would  also  be  well. 

t  By  all  means  have  the  pupils  see  this  and  all  kindred  facts  exemplified 

with  the  measures  themselves. 

{j°$ 

IVEE 

or 

f> 


136 


SIMPLE    LESSONS   IN 


DENOMINATE   NUMBERS.  137 

Abbreviations. — pk.  stands  for  peck,  or  pecks;  and  bu. 
for  bushel,  or  bushels. 

3.  Do  you  think  a  common  wooden  water-pail  will  hold 
a  bushel  ?    Will  it  hold  a  half-bushel  ?    Will  it  hold  a 
peck  ?  * 

4.  How  many  common  wooden  water-pail fuls  of  corn 
do  vou  think  it  would  take  to  fill  a  bushel  basket  ? 

t/ 

5.  Do  you  think   you   could  carry  a  peck   of  corn  ? 
Could  you  carry  a  bushel  ?     Two  bushels  ? 

6.  You  have  seen  flour-barrels,  have  you  not  ?     How 
many  bushels  do  you  think  a  flour-barrel  holds?     2  bu.  ? 

3  bu.  ?     4  bu.  ?  f 

7.  Do  you  think  that  a  boy  can  put  a  peck  of  nuts  in 
his  pocket?     Can  he  put  a  bushel  of  nuts  in  his  pocket? 
Can  he  put  a  quart  in  ?    A  pint  ? 

8.  How  many  pints  does  it  take  to  make  a  peck  ? 

9.  How  many  pecks  in  5  ~bu.  ? 

10.  How  many  half-bushel  measures  full  does  it  take 
to  fill  a  two-bushel  bag  ? 

11.  If  I  want  to  measure  out  a  bushel  of  wheat  and 
have  only  a  quart  cup  to  do  it  with,  how  many  cupfuls 
must  I  take  ? 

12.  If  I  wish  to  measure  out  5-^  bu.  of  corn,  how  many 
times  must  I  fill  the  half-bushel  measure  ? 

13.  What  part  of  a  quart  is  a  pint  ? 

14.  What  part  of  a  peck  is  a  quart  ? 

15.  What  part   of  a  peck   is  2  qt.?     Three  quarts? 

4  qt.  ?     5  qt.  ?     6  qt.  ?     7  qt.  ?     8  qt.  ? 

*  Such  a  pail  holds  about  10  liquid  quarts,  or  about  a  pint  over  a  peck. 

t  Such  a  barrel  is  27  inches  deep  and  about  18  inches  in  diameter,  and  hence 
holds  about  104  dry  quarts. 


138 


SIMPLE    LESSONS   IN 


16.  What  part  of  a  bushel  is  a  peck  ?     2  pJc.  ?     3  pJc.  ? 

17.  How  many  pecks  in  a  half-bushel  ? 

18.  How  many  times  will  you  have  to  fill  the  4-quart 
measure  to  make  a  half-bushel  ?    How  many  times  to 
make  a  bushel  ? 


Fifth  Exercise. 
WEIGHTS  AND   WEIGHING. 

1.  If  you  were  to  go  to  the  grocery  to  buy  some  tea, 
coffee,  or  sugar,  how  would  you  tell  the  groceryman  how 
much  you  wanted  ?  Would  you  tell  him  that  you  wanted 
a  pint  of  tea,  or  a  yard  of  coffee,  or  a  gallon  of  sugar  ? 
How  would  you  tell  him  ?  Would  a  pound  of  sugar  fill  a 
gallon  measure  ?  Which  measure  do  you  think  a  pound 
of  sugar  would  come  nearest  to  filling — a  pint,  quart,  or 
gallon  measure  ?  What  would  the  groceryman  use  to  de- 
termine how  much  sugar  he  gave  you  ?  (Scales.) 


2.  Learn  this 

TABLE  OF  AVOIRDUPOIS*  WEIGHTS. 

16  ounces  =  1  pound. 

100  pounds  =  1  hundred-weight. 

20  hundred-weight  =.  1  ton. 

*  If  the  teacher  thinks  best,  she  can  explain  that  this  long  word  is  three 
French  words  (avoir  dupoida)  put  together,  and  means  to  have  weight. 


DENOMINATE    NUMBERS.  139 

Abbreviations. — oz.  stands  for  ounce,  or  ounces;  Ib.  for 
pound,  or  pounds;  cwt.  for  hundred-weight;  and  T.  for 
ton,  or  tons. 

3.  How  many  5-cent  nickels  do  you  think  it  takes  to 
make  an  ounce  ?  *     How  many  to  make  a  pound  ? 

4.  How  much  do  you  think  a  pint  of  water  weighs  ?f 
It  weighs  just  about  a  pound.     How  many  ounces,  then, 
does  a  common  teacupful  of  water  weigh  ?     What  part 
of  a  pound  ? 

5.  How  much  does  a  quart  of  water  weigh  ?  J     How 
much  does  a  gallon  of  water  weigh  ?     How  much  does  a 
common  wooden  pailful  of  water  weigh  ?     You  remember 
that  we  learned  that  such  a  pail  holds  about  10  quarts. 

6.  How  much  do  you  weigh  ?     Do  you  weigh  a  ton  ? 
A  hundred-weight  ?     How  many  boys  who  weigh  50  Ib. 
each  does  it  take  to  weigh  a  hundred-weight  ?  §     How 
many  to  weigh  a  ton  ? 

7.  Did  you  ever  see  a  large  load  of  hay  drawn  by  two 
horses  ?     Do  you  think  such  a  load  weighs  a  hundred- 
weight ?   Do  you  think  a  span  of  horses  could  draw  a  ton 
of  hay  ?    Can  a  span  of  horses  draw  a  ton  of  boys  and  girls  ? 

8.  How  many  ounces  in  a  pound  ?     How  many  in  a 
half-pound  ?    How  many  in  a  quarter  of  a  pound  ? 

9.  Four  ounces  is  what  part  of  a  pound  ?   8  oz.  is  what 
part  of  a  pound  ?     2  oz.  is  what  part  of  a  pound  ? 

*  An  avoirdupois  ounce  =  437.5  grains,  and  a  5-cent  nickel  weighs  77.16  grs. 

t  A  quart  weighs  2.0843  +  Ibs.  A  pint  of  water,  therefore,  is  an  excellent 
object  with  which  to  teach  the  pupil  what  a  pound  is. 

%  Teach  them  to  say  nearly  in  such  cases  ;  also  that  the  vessel  is  not  included. 

§  This  is  beyond  what  the  pupil  has  been  taught ;  but  it  affords  so  good  an 
illustration,  that  it  will  be  well  for  the  teacher  to  explain  it;  first,  however,  let- 
ting the  class  try  their  full  strength  on  it.  Very  likely  they  can  get  it  out. 


140 


SIMPLE    LESSONS    IN 


10.  How  many  %-oz.  weights  would  it  take  to  make  a 
pound  ?     How  many   4-03.  weights  ?     How   many   8-02. 
weights  ? 

11.  How  many  ounces  in  f  Ib.  ?     How  maoy  in  1J  Ib.  ? 

12.  Four  ounces  and  5  ounces  and  six  ounces  together 
lack  how  many  ounces  of  being  a  pound  ? 

13.  How  many   hundred-weight  make  a  ton?     How 
many  make  a  quarter  of  a  ton  ?    How  many  make  a  half 
ton  ?     40  cwt.  are  how  many  tons  ? 


Sixth  Exercise. 
WEIGHING   WITH  BALANCE.* 

1.  Here  is  a  Balance. 
It  is  the  simplest  ma- 
chine used  for  weigh- 
ing ?   All  you  have  to 
do  is  to  put  into  one 
pan  such  weights  as 
are     equal     to     the 
amount    you    want 
to  weigh,  and  pour 
the     thing     to      be 
weighed     into     the 
other   pan    till    the 
pans  balance. 

2.  If  the  man  in  the  picture  has  a  2-pound  weight  and 

*  The  purpose  of  this  and  the  two  following  exercises  is  to  teach  the  pupils 
how  to  weigh.  Every  primary  school  should  have  a  balance  with  weights,  a 
pair  of  steel-yards,  and  a  set  of  grocer's  scales,  and  the  pupils  should  be  taught 
to  use  them. 


DENOMINATE    NUMBERS.  141 

a  4-pound  weight  in  one  pan,  how  much  coffee  will  he 
have  in  the  other  to  make  them  balance  ? 

3.  I  wanted  to  find  out  how  much  a  dressed  chicken 
weighed,  and  put  it  into  one  pan,  and  then  put  into  the 
other  pan  a  2-pound  weight,  and  a  1-pound  weight,  and 
an  S-oz.  weight,  and  a  4-03.  weight.    How  much  did  the 
chicken  weigh  ? 

4.  On  weighing  a  turkey,  I  found  that  I  had  a  5-pound 
weight,  a  2-pound  weight,  a  1-pound  weight,  and  an  S-oz. 
weight.    How  much  did  the  turkey  weigh  ? 

5.  A  grocer,  in  weighing  a  roll  of  butter,  put  on  a  %-lb. 
weight,  a  \-lb.  weight,  an  8-02.  weight,  and  a  4-02.  weight. 
He  said  the  butter  weighed  If  lb.  ?    Was  he  right  ? 


Seventh  Exercise. 
WEIGHING  WITH   STEEL-YARDS. 


il       l!0 


1.  Here  is  a  pair  of  steel-yards  for  weighing.    A  pail  of 
butter  is  being  weighed.     You  see  that  the  pail  is  hung 

7 


142  SIMPLE    LESSONS   IN 

on  the  hook  nearest  the  large  end  of  the  bar,  and  the 
man  holds  it  up  by  one  of  the  other  hooks.  If  you  were 
to  take  the  small  weight  off  the  long  bar,  would  the  pail 
of  butter  stay  up  ?  The  small  weight  balances  the  large 
pail  of  butter  just  as  a  small  boy  can  balance  a  large  one 
on  a  see-saw.  How  is  that  ?  If  you  put  the  weight  nearer 
the  hook,  how  will  the  steel-yards  act  ?  If  you  put  it 
further  away  than  it  now  is  ?  At  what  figure  does  the 
weight  balance  the  butter?  Then  the  pail  and  butter 
weigh  how  much  ?  * 

2.  Count  the  large  divisions  of  the  bar.     Each  of  these 
indicates  a  pound.     Into  how  many  small  divisions  is 
each  of  the  larger  divisions  divided  ?     One-eighth  of  a 
pound  is  how  many  ounces  ?     Then  each  of  the  small  di- 
visions indicates  how  many  ounces  ? 

3.  In  weighing  a  package,  I  found  that  the  steel-yards 
balanced  when  the  small  weight  was  at  the  middle  mark 
between  5  and  6.     How  much  did  the  package  weigh  ? 

4.  How  much  does  a  package  weigh  which  requires  the 
weight  to  be  2  small  divisions  beyond  10  toward  the  end 
of  the  bar,  to  balance  it  ?     How  much  if  the  weight  is 
between  7  and  8  and  within  2  divisions  of  8  ?   How  much 
if  it  is  within  3  divisions  of  8  ? 

5.  If  your  pail  weighs  2  Ib.  and  you  want  5  lb.  of  butter, 
where  will  the  small  weight  be  on  the  arm  when  you  have 
enough  in  the  pail  ? 

6.  Where  must  the  small  weight  be  so  that  you  shall 
have  4  Ib.  in  the  pail,  if  the  pail  weighs  \\  Ib.  ? 


*  Doubtless  a  fuller  explanation  may  be  needed  for  many  pupils,  but  the 
teacher  can  readily  supply  it,  having  the  instrument  before  them. 


DENOMINATE    NUMBERS. 


143 


Eighth  Exercise. 


WEIGHING    WITH    SCALES. 


i\/T 


as  >»  «F 


'  1 


1.  Here  are  three  sorts 
of  weighing  machines. 
The  upper  one,  on  the 
counter,  is  the  common 
grocer's  scales.  You  can 
see  them  at  the  grocery- 
store..  The  things  to  be  weighed  are  put  into  the  scale- 
pan,  and  then  the  small  weight  is  moved  on  the  bar  till  it 
balances  what  is  in  the  pan.  There  are  figures  on  the 
bar  just  as  on  the  steel-yards,  by  which  you  can  tell  how 
much  is  weighed.* 


*  If  the  teacher  has  no  scales,  it  will  create  much  interest  and  good  feeling 
to  take  the  little  ones  to  the  store  where  these  can  be  seen,  and  let  them  learn 
how  they  work. 


144  SIMPLE    LESSONS   IN 

2.  The  scales  in  the  left-hand  side  of  the  picture  are 
called  platform  scales.    The  little  girl  who  is  standing  on 
the  platform  of  the  scales  is  being  weighed.     The  man  is 
moving  the  small  weight  on  the  bar  to  find  just  where  it 
balances,  as  you  do  011  the  bar  of  the  steel-yards.     How 
much  do  you  think  the  little  girl  will  weigh  ?     May  be 
your  teacher  can  go  with  you  to  some  place  where  they 
have  such  scales  and  teach  you  how  to  weigh  each  other. 
Such  scales  are  used  for  weighing  heavy  articles,  like  bar- 
rels of  flour,  quarters  of  beef,  dressed  hogs,  etc. 

3.  The  other  scales  in  the  picture  are  called  hay-scales. 
You  see  that  they  are  just  like  the  platform-scales,  only 
larger.     The  platform  is  large  enough  so  that  a  wagon 
loaded  with  hay  can  stand  on  it.     The  man  stands  at  the 
bar  to  put  the  weight  in  the  right  place  to  make  it  bal- 
ance.    You  see  that  the  wagon  is  weighed  with  the  hay. 
How  shall  the  man  find  out  how  much  the  hay  weighs 
without  the   wagon?     If  the  wagon  and  hay  together 
weigh  29  civt.,  and  the  wagon  alone  weighs  7  cwt.,  is 
there  a  ton  of  hay  ?  * 

4.  If  the  little  girl  on  the  platform  scales  has  a  pack- 
age in  her  left  hand  which  weighs  3  lb.,  and  the  man 
finds  that  she,  with  the  package,  weighs  48  lb.,  how  much 
does  the  girl  weigh  ? 

5.  If  the  groceryman  puts  up  for  me  5  lb.  of  sugar 
worth  9  cents  per  pound,  how  much  must  I  pay  him  ? 


*  Such  question?  which  are  a  little  in  advance  of  the  pupils'  study  should  be 
thrown  in  occasionally  to  create  or  keep  alive  a  desire  to  go  forward  and  learn 
dew  things. 


DENOMINATE    NUMBERS, 


145 


Ninth  Exercise. 
MEASURES  OF   TIME. 

1.  Here  is  a  picture  of  a  clock- 
face.     How  many  numbers  are 
there    around    it?     Into   how 
many  equal  parts  is  the  ring 
around  the  edge  divided  by  the 
heavy  marks  ?     Into  how  many 
equal  parts  are  the  spaces  be- 
tween the  heavy  marks  divided 
by  the  light  marks  ? 

2.  How  many  pointers  are  there  on  the  face  of  the 
clock?     Are  both   of  the  same  length?     Which  is  the 
longer,  the  one  which  points  to  3  or  the  one  which  points 
to  12  ?     These  pointers  are  called  hands.    You  can  watch 
the  clock  and  see  that  the  hands  move  around  the  face. 
The  long  hand  is  called  the  Minute  Hand,  and  the  short 
one  the  Hour  Hand.    To  what  number  does  the  minute 
hand  point  ?   To  what  number  does  the  hour  hand  point  ? 
Show  in  each  of  the  clock-faces  in  the  next  exercise  which 
is  the  minute  hand  and  which  the  hour  hand. 

3.  Watch  the  clock  in  the  room  a  little  while  and  see 
which  hand  goes  the  faster.     Can  you  see  either  of  them 
go  ?     Watch  the  minute  hand  awhile  and  see  if  it  does 
not  go.     Which  goes  the  faster  ?     See  how  many  you  can 
count  while  the  minute  hand  is  going  from  one  of  the 
fine  marks  to  the  next.     Can  you  count  a  hundred  while 
the  minute  hand  goes  over  one  of  these  small  spaces  ?    It 
takes  it  just  1  minute  to  go  over  one  of  these  spaces. 


146  SIMPLE    LESSONS   IN 

4.  Is  a  minute  a  long  time,  or  a  short  time  ?   Could  you 
go  home  in  a  minute  ?     Could  you  go  to  the  door  and 
back  in  a  minute  ? 

5.  If  it  takes  the  minute  hand  1  minute  to  go  over  one 
of  the  small  spaces,  how  long  will  it  take  it  to  go  from  12 
to  1  ?     From  1  to  2  ?     From  2  to  3  ?     How  long  to  go    . 
from  12  to  6  ?     How  long  to  go  from  12  to  3  ?   How  long 
to  go  clear  around  ? 

6.  If  you  can  have  patience  to  watch,  you  will  find  that 
the  hour  hand  goes  from  any  figure  to  the  next  while  the 
minute  hand  goes  clear  around.    It  is  just  an  Hour  while 
the  hour  hand  is  going  from  any  figure  to  the  next  one. 
How  many  minutes  in  an  hour  ? 

7.  How  long  does  it  take  the  minute  hand  to  go  from 
12  to  3  ?     What  part  of  the  whole  way  around  is  it  from 
12  to  3  ?     How  many  minutes  in  a  quarter  of  an  hour  ? 

8.  How  long  does  it  take  the  minute  hand  to  go  from 
12  to  1  ?     How  many  times  as  long  does  it  take  it  to  go 
from  12  to  6  ?     How  many  minutes  does  it  take  for  the 
minute  hand  to  go  from  12  to  6  ?     How  many  minutes  in 
half  an  hour  ? 

9.  How  many  minutes  does  it  take  the  minute  hand 
to  go  from  12  to  2  ?     From  12  to  4  ?    From  12  to  5  ? 
From  11  to  12  ?     From  10  to  12  ?    From  9  to  12  ?    From 
8  to  12?     From  7  to  12? 

10.  From  midnight  to  noon  the  hour  hand  goes  just 
once  around  from  12  to  12.     How  long  does  it  take  the 
hour  hand  to  go  from  12  to  1  ?    From  1  to  2  ?     How 
many  hours  to  go  clear  around  ?     Then  from  noon  to 
midnight  the  hour  hand  goes  around  again.     How  many 
hours  is  it  from  noon  to  midnight  ? 


DENOMINATE    NUMBERS. 


147 


11.  From  midnight  to  midnight  again  is  called  a  day. 
How  many  hours  in  such  a  day  ?    About  how  much  of 
the  day  is  it  light  ?     About  how  much  is  it  dark  ? 

12.  If  you  have  some  kernels  of  corn  in  a  cup  and 
count  them  out  one  by  one,  picking  them  out  with  your 
fingers  and  laying  them  on  the  table  as  fast  as  you  con- 
veniently can,  you  will  find  that  you  can  count  out  about 
60  in  a  minute.    If  you  count  out  just  60  in  a  minute,  the 
time  it  takes  you  to  count  out  1  is  a  second.    How  many 
seconds  in  a  minute  ? 

13.  Learn  the  following 

TABLE  OF  MEASURES  OF  TIME. 

60  seconds    =  1  minute. 
60  minutes  =  1  hour. 
24  hours      =  1  day. 


Tenth  Exercise. 
HOW  TO  TELL  THE  TIME  OF  DAY  BY  THE  CLOCK. 

1.  At  noon  the  hands  are 
both  together  at  the  number 
12.  It  is  then  12  o'clock.  One 
hour  after  noon  the  hour  hand 
has  gone  on  to  1,  and  the  min- 
ute hand  has  gone  clear  around. 
It  is  then  1  o'clock.  When  the 
hour  hand  is  at  2,  where  is  the 
minute  hand  ?  What  o'clock 


148 


SIMPLE   LESSONS   IN 


is  it  then  ?  What  o'clock  is  it  when  the  hands  are  as  on 
page  145  ?  How  long  after  12  o'clock  is  3  o'clock  ?  What 
time  is  it  when  the  hands  are 
as  in  this  picture  ?  How  long 
is  it  from  8  o'clock  on  to  12 
o'clock  ?  * 

2.  What  time  is  it  when  the 
minute  hand  is  at  12,  and  the 
hour  hand  at  10  ? 

3.  Where  is  the  hour  hand 
in  this  picture  ?    Is  it  before  or 
after  11  ?   When  the  hour  hand 
was  at  11,  where  was  the  min- 
ute hand  ?    How  many  min-  £ 
utes  does  it  take   the  minute 
hand  to  go  from  12  to  where  it  is 
in  this  picture  ?  How  many  min- 
utes is  it  then  past  11  o'clock  ? 

4.  What  hour  is  the   hour 
hand  nearest  in  this  picture? 
Is  it  before  or  after  2  o'clock  ? 
How  long  will  it  take  the  min- 
ute hand  to  get  from  where  it 
is  to  12  ?     Where  will  the  hour 
hand  be  then  ?   What  time  will 
it  be  then  ?     Then  what  time 
is  indicated  in   this    picture? 
How  long  before  2  o'clock  ? 

*  These  and  the  following  are  only  given  as  specimen  questions  indicating 
the  manner  of  procedure. 


DENOMINATE    NUMBERS. 


149 


5.  What  hour  is  the  hour 
hand  in  this  picture  nearest? 
Is  it  before  or  after  5  o'clock  ? 
How  long  will  it  take  the  min- 
ute hand  to  get  from  where  it 
is  to  8  ?  How  long  to  get  from 
8  to  12  ?  Then  how  long  will 
it  take  the  minute  hand  to  get 
from  where  it  is  in  the  picture 
to  12  ?  Where  will  the  hour  hand  be  then  ?  How  long 
is  it  then  before  5  o'clock  ? 


Concluding   Lesson. 

1.  DAYS  OF  THE  WEEK. — How  many  days  in  a  week  ? 
What  are  their  names  ?    Ans.  Sunday,  Monday,  Tues- 
day, Wednesday,  Thursday,  Friday,  Saturday.    What  day 
comes  after  Tuesday?    What  day  comes  before  Friday? 
What  day  conies  after  Thursday  ? 

2.  MONTHS. — A  month  is  generally  a  little  more  than 
4  weeks.   How  many  months  are  there  in  a  year  ?   Ans.  12. 
Name  the  months  thus :  January,  February,  March,  April, 
May,  June,  July,  August,  September,  October,  November, 
December.    What  month   comes   after   March  ?     What 
month  after  October  ?     What  before  July  ?    What  before 
May? 

3.  The  months  are  not  all  of  the  same  length,  but  this 
little  verse  will  enable  you.  to  remember  the  number  of 
days  in  each : 


150  DENOMINATE   NUMBERS. 

Thirty  days  hath  September, 
April,  June,  and  November. 
By  one  more  others  vary, 
Save  the  month  February  : 
Twenty-eight  this  receiveth, 
Until  leap-year*  one  more  giveth. 

4.  How  many  months  have  30  days  each  ?  How  many 
have  31  days  each  ?   Which  is  the  shortest  month  ?   How 
many  days  has  the  shortest  month  ? 

5.  Which  month  is  usually  just  4  weeks  long?    How 
many  days  over  4  weeks  do  the  long  months  have  ?    In 
how  many  places  do  two  long  months  come  together  ? 

6.  January  has  how  many  days  ? 
February  has  how  many  days  ? 
March  has  how  many  days  ? 
April  has  how  many  days  ? 
May  has  how  many  days  ? 
June  has  how  many  days  ? 
July  has  how  many  days  ? 
August  has  how  many  days  ? 
September  has  how  many  days  ? 
October  has  how  many  days  ? 
November  has  how  many  days  ? 
December  has  how  many  days  ? 

7.  Now  who  of  you  all  can  tell  how  many  31  +  28  +  31 
+  30.+ 31  +  30  +  31  +  31  +  30 +  31+ 30  +  31  make? 
That  is,  how  many  days  are  there  in  a  year  ?    This  is  a 
pretty  difficult  question  for  you,  and  you  have  not  been 
taught  in  this  book  how  to  solve  it.     But  the  next  book 

will  teach  you  this  and  much  more  about  numbers. 

— . _ __ — _ — __ — 

*  The  teacher  should  explain  what  is  meant  by  leap-year— i.  e.,  in  general, 
every  4th  year. 

. 

It 
V     >*  oar 

*  T 


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